Question 1 :
$\displaystyle \Delta = \begin{vmatrix}1 & \log_{x}y  & \log_{x}z \\ \log_{y}x & 1 & \log_{y}z \\ \log _{z}x  &\log _{z}y  & 1\end{vmatrix}$ is equal to <br/> <br/>
Question 2 :
If $A$ is a $3\times 3$ matrix and $\text{det}  (3A)=k(\text{det}  A)$, then $k=$
Question 3 :
Find the value of the following determinant:<br/>$\begin{vmatrix}\displaystyle \frac{-4}{7} & \displaystyle \frac{-6}{35}\\ 5 & \displaystyle \frac{-2}{5}\end{vmatrix}$
Question 4 :
Let the matrix A and B be defined as $A =\begin{vmatrix} 3 & 2 \\ 2 & 1 \end{vmatrix}$ and $B =\begin{vmatrix} 3 & 1 \\ 7 & 3 \end{vmatrix}$ then the value of Det.$(2A^9B^{-1})$, is
Question 5 :
Find the value of the following determinant:<br/>$\begin{vmatrix}3\sqrt{6} & -4\sqrt{2}\\ 5\sqrt{3} & 2\end{vmatrix}$
Question 6 :
$\mathrm{If}$ $\left|\begin{array}{lll}<br>1 & 0 & 0\\<br>2 & 3 & 4\\<br>5 & -6 & x<br>\end{array}\right|$ $= 45$ $\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}$ $\mathrm{x}=$<br><br>
Question 7 :
If $\begin{vmatrix} a & a & x\\ m & m & m\\ b & x & b\end{vmatrix}=0$ then $x=?$
Question 8 :
If the trivial solution is the only solution of the system of equations$x-ky+z=0,kx+3y-kz=0, 3x+y-z=0$. Then the set of all values of k is:<br>
Question 9 :
Let a, b, c be three complex numbers, and let<br>$z=\begin{vmatrix}<br>0 & -b & -c\\ <br>b & 0 & -a\\ <br>c & a & 0<br>\end{vmatrix}$<br>then z equal<br>
Question 10 :
$\begin{vmatrix} 2^3 & 3^3 & 3.2^2+3.2+1\\ 3^3 & 4^3 & 3.3^2+3.3+1\\ 4^3 & 5^3 & 3.4^2+3.4+1\end{vmatrix}$ is equal to?
Question 11 :
If $x, y, z$ are positive numbers, then value of the determinant $\begin{vmatrix}1 & log_xy & log_xz \\ log_yx & 1 & log_yz\\ log_zx & log_zy & 1\end{vmatrix}$ is equal to<br/>
Question 12 :
The determinant $\displaystyle \left | \begin{matrix}<br>y^{2} & -xy &x^{2} \\ <br>a& b &c \\ <br>a'&b' & c'<br>\end{matrix} \right |$ is equal to<br>
Question 13 :
If $\begin{vmatrix}p& q - y& r - z\\ p - x& q & r - z\\ p - x& q - y& r\end{vmatrix} = 0$, then the value of $\dfrac {p}{x} + \dfrac {q}{y} + \dfrac {r}{z}$ is<br>
Question 14 :
$|f(x)|={\begin{bmatrix}{}<br/>\mathrm{s}\mathrm{i}\mathrm{n}x & \mathrm{c}\mathrm{o}\mathrm{s}ecx & \mathrm{t}\mathrm{a}\mathrm{n}x\\<br/>\mathrm{s}\mathrm{e}\mathrm{c}x & x\mathrm{s}\mathrm{i}\mathrm{n}x & x\mathrm{t}\mathrm{a}\mathrm{n}x\\<br/>x^{2}-1 & \mathrm{c}\mathrm{o}\mathrm{s}x & x^{2}+1<br/>\end{bmatrix}}$ then . $.\displaystyle \int_{-a}^{a}|f(x)|d$ equals <br/><br/><br/>
Question 15 :
The sum of infinite series$\begin{vmatrix}<br>1 &2 \\ <br>6 & 4<br>\end{vmatrix}+\begin{vmatrix}<br>\frac{1}{2} &2 \\ <br> 2& 4<br>\end{vmatrix}+\begin{vmatrix}<br>\frac{1}{4} & 2\\ <br> \frac{2}{3}& 4<br>\end{vmatrix}+$.......is
Question 16 :
Simplify $\triangle = $ <br> $<br/>\left |<br/>\begin{array}{111}<br/>1 & sin3\theta & sin^3\theta \\<br/> 2cos\theta& sin6\theta & sin^32\theta \\<br/>4cos^2\theta & sin9\theta & sin^33\theta \\<br/>\end {array}<br/>\right |<br/>$ equals
Question 17 :
$A=\left[ \begin{matrix} 5 & 5\alpha & \alpha \\ 0 & \alpha & 5\alpha \\ 0 & 0 & 5 \end{matrix} \right] $; If $\left| { A }^{ 2 } \right| =25$, then $\left| \alpha \right| =$
Question 18 :
The value of the determinant $\displaystyle \left | \begin{matrix}<br/>1 &\omega ^{3}  &\omega ^{5} \\ <br/> \omega ^{3}&1  &\omega ^{4} \\ <br/> \omega ^{5}&\omega ^{4}  &1 <br/>\end{matrix} \right |$ , where $\omega$ is an imaginary cube root of unity,is<br/>
Question 19 :
$\left|\begin{array}{lll}<br>\mathrm{a}+\mathrm{b} & \mathrm{a} & \mathrm{b}\\<br>\mathrm{a} & \mathrm{a}+\mathrm{c} & \mathrm{c}\\<br>\mathrm{b} & \mathrm{c} & \mathrm{b}+\mathrm{c}<br>\end{array}\right|=$<br>
Question 20 :
<br>The value of the determinant $\begin{vmatrix}b^{2}-ab\,\, b-c\,\, bc-ac & & \\ ab-a^{2}\,\, a-b\,\, b^{2}-ab& & \\ bc-ac\,\, c-a\,\, ab-a^{2}& & \end{vmatrix}$ =
Question 21 :
If the determinant of the adjoint of a (real) matrix of order 3 is 25, then the determinant of the inverse of the matrix is.<br>
Question 22 :
If a$\neq$ b $\neq$ c are all positive, then the value of the determinants $\begin{vmatrix} a & b & c \\ b & c & a\\ c & a & b\end{vmatrix}$ is.<br>
Question 23 :
If A = $\begin{bmatrix}<br/>a & b\\ <br/> c& d<br/>\end{bmatrix}$ (where $b\neq c$) and satisfies the equation $A^{2}+kI=0$, then <br/>
Question 24 :
The determinant $\begin{vmatrix} { y }^{ 2 } & -xy & { x }^{ 2 } \\ a & b & c \\ a' & b' & c' \end{vmatrix}$ is equivalent to<br/>
Question 25 :
The sum of the real roots of the equation<br>$\begin{vmatrix} x & -6 & -1 \\ 2 & -3x & x-3 \\ -3 & 2x & x+2 \end{vmatrix}=0$ is equal to
Question 26 :
Let $M$ and $N$ be two $3 \times3$ matrices such that $ MN = NM$. Further, if $M \neq$ $N^2$ and $M^2= N^4$, then
Question 27 :
Consider the following statements:<br>$1$. Determinant is a square matrix.<br>$2$. Determinant is a number associated with a square matrix.<br>Which of the above statements is/are correct?<br>
Question 30 :
The values of the determinant$\begin{vmatrix}1 &e^{\tfrac{i\pi}{3}}  &e^{\tfrac{i\pi}{4}} \\e^{-\tfrac{i\pi}{3}} & 1 &e^{\tfrac{2i\pi}{3}} \\e^{-\tfrac{i\pi}{4}} &e^{-\tfrac{2i\pi}{3}}  &1\end{vmatrix}$ is
Question 31 :
If$\displaystyle \begin{vmatrix} x & 1 \\ y & 2 \end{vmatrix} $-$\displaystyle \begin{vmatrix} y & 1 \\ 8 & 0 \end{vmatrix} $=$\displaystyle \begin{vmatrix} 2 & 0 \\ -x & 2 \end{vmatrix} $ then the values of x and y respectively are
Question 32 :
If every row of a matrix $A$ contains $p$ elements and its column contains $q$ elements, then the order of $A$ is
Question 33 :
The order of the matrix $A$ is $3\times 5$ and that of $B$ is $2\times 3$. The order of the matrix $BA$ is:
Question 34 :
The number of possible orders of a matrix containing $24$ elements are:
Question 35 :
If $A+B = \begin{bmatrix}1 & 0 \\ 1 & 1\end{bmatrix}$ and $A-2B = \begin{bmatrix}-1 & 1 \\ 0 & -1\end{bmatrix}$, then $A$ =
Question 36 :
The value of x satisfying the equation 2$\displaystyle \begin{vmatrix} 3 & 1 \\ 1 & 2 \end{vmatrix} $+$\displaystyle \begin{vmatrix} x^{2} & 9 \\ -1 & 0 \end{vmatrix} $=$\displaystyle \begin{vmatrix} 5x & 6 \\ 0 & 1 \end{vmatrix} $+$\displaystyle \begin{vmatrix} 0 & 5 \\ 1 & 3 \end{vmatrix} $are
Question 39 :
Suppose $A$ is any $3\times 3$ non-singular matrix and $(A-3I)(A-5I)=O$, where $I=I_{3}$ and $O=O_{3}$, If $\alpha A+\beta A^{-1}=4I$, then $\alpha+\beta$ is equal to :
Question 40 :
The order the matrix is $ \begin{bmatrix}2 & 3 & 4 \\ 9 & 8 & 7 \end{bmatrix}$ is <br/>
Question 41 :
The Inverse of a square matrix, if it exist is unique.
Question 42 :
If $2A-\begin{bmatrix} 1 & 2 \\ 7 & 4 \end{bmatrix}=\begin{bmatrix} 3 & 0 \\ 0 & -2 \end{bmatrix}$, then $A$ is equal to-
Question 43 :
The number of all possible matrices of order $3 \times 3$ with each entry $0$ or $1$ is:
Question 44 :
If $A=\displaystyle \left[ \begin{matrix} 1 &2 \\ 3& 4 \end{matrix} \right] $, then which of the following is not an element of $A$?
Question 45 :
<b>If $A$ is a square of order $3$, then</b> $\left| Adj\left( Adj{ A }^{ 2 } \right)\right| =$
Question 46 :
If$\displaystyle \begin{vmatrix} 2 & 3 \\ 4 & 4 \end{vmatrix} $+$\displaystyle \begin{vmatrix} x & 3 \\ y & 1 \end{vmatrix} $=$\displaystyle \begin{vmatrix} 10 & 6 \\ 8 & 5 \end{vmatrix} $,then (x,y)=
Question 47 :
$\displaystyle { A=\left[ { a }_{ ij } \right] }_{ m\times n}$ is a square matrix , if
Question 48 :
If $\displaystyle  \begin{vmatrix} x & y   \\ 1 & 6   \end{vmatrix} $ = $\displaystyle  \begin{vmatrix} 1 & 8   \\ 1 & 6   \end{vmatrix} $ then x+2y=
Question 49 :
Construct the matrix of order $3 \times 2$ whose elements are given by $a_{ij} = 2i - j$
Question 50 : A word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as in the two matrices given below. The columns and rows of Matrix I are numbered from $0$ to $4$ and that of Matrix II are numbered from $5$ to $9$. A letter from these matrices can be represented first by its row and next by its column, e.g., $'R'$ can be represented by $04, 42$ etc., and $'D'$ can be represented by $57, 76$ etc. Similarly, you have to identify the set for the word 'ROAD'.<table class="wysiwyg-table"><tbody><tr><td></td><td></td><td>Matrix I</td><td></td><td></td><td></td></tr><tr><td></td><td>$0$</td><td>$1$</td><td>$2$</td><td>$3$</td><td>$4$</td></tr><tr><td>$0$</td><td>$F$</td><td>$O$</td><td>$M$</td><td>$S$</td><td>$R$</td></tr><tr><td>$1$</td><td>$S$</td><td>$R$</td><td>$F$</td><td>$O$</td><td>$M$</td></tr><tr><td>$2$</td><td>$O$</td><td>$M$</td><td>$S$</td><td>$R$</td><td>$F$</td></tr><tr><td>$3$</td><td>$R$</td><td>$F$</td><td>$O$</td><td>$M$</td><td>$S$</td></tr><tr><td>$4$</td><td>$M$</td><td>$S$</td><td>$R$</td><td>$F$</td><td>$O$</td></tr></tbody></table><table class="wysiwyg-table"><tbody><tr><td></td><td></td><td>Matrix II</td><td></td><td></td><td></td></tr><tr><td></td><td>$5$</td><td>$6$</td><td>$7$</td><td>$8$</td><td>$9$</td></tr><tr><td>$5$</td><td>$A$</td><td>$T$</td><td>$D$</td><td>$I$</td><td>$P$</td></tr><tr><td>$6$</td><td>$I$</td><td>$P$</td><td>$A$</td><td>$T$</td><td>$D$</td></tr><tr><td>$7$</td><td>$T$</td><td>$D$</td><td>$I$</td><td>$P$</td><td>$A$</td></tr><tr><td>$8$</td><td>$P$</td><td>$A$</td><td>$T$</td><td>$D$</td><td>$I$</td></tr><tr><td>$9$</td><td>$D$</td><td>$I$</td><td>$P$</td><td>$A$</td><td>$T$</td></tr></tbody></table>
Question 51 :
If A=$\displaystyle \begin{vmatrix} 2 & -3 \\ 3 & 2 \end{vmatrix} $ and B=$\displaystyle \begin{vmatrix} 3 & -2 \\ 2 & 3 \end{vmatrix} $ then 2A-B=
Question 52 :
The order of a matrix $\begin{bmatrix} 2& 5& 7\end{bmatrix} $ is 
Question 53 :
If $A = \begin{bmatrix}1\end{bmatrix}$, then the order of the matrix is
Question 54 :
The entries of a matrix are integers. Adding an integer to all entries on a row or on a column is called an operation. It is given that for infinitely many integers N one can obtain, after a finite number of operations, a table with all entries divisible by N. Prove that one can obtain, after a finite number of operations, the zero matrix.
Question 55 :
If $\begin{bmatrix}x & 0 \\ 1 & y\end{bmatrix} +\begin{bmatrix}-2 & 1 \\ 3 & 4\end{bmatrix} =\begin{bmatrix}3 & 5 \\ 6 & 3\end{bmatrix} -\begin{bmatrix}2 & 4 \\ 2 & 1\end{bmatrix}$, then
Question 56 :
If $A = \begin{bmatrix} 0 & 2 & 3 \\ 3 & 5 & 7 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 & 7 \\ 2 & 4 & 1 \end{bmatrix}$,  if $A+B = \begin{bmatrix} 1 & 5 & 10 \\ 5 & k & 8 \end{bmatrix} \\ $<br/>Find the value of k 
Question 57 :
What is the order of the product $ \begin{bmatrix} x &  y & z \end{bmatrix} \begin{bmatrix} a & h & g \\ h & b & f \\ g & f & c \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix}$ ?
Question 58 :
If $A = \displaystyle \left[ \begin{matrix} 1 &2 \\ 3& 4 \end{matrix} \right] $, then number of elements in $A$ are
Question 59 :
If order of a matrix is $3 \times 3$, then it is a
Question 60 :
If for a matrix $\displaystyle A,{ A }+I=O$, where $I$ is an identity matrix, then $A$ equals
Question 61 :
If $A = \begin{bmatrix}1 & -2 \\ 3 & 0\end{bmatrix}, \space B = \begin{bmatrix}-1 & 4 \\ 2 & 3\end{bmatrix},\space C = \begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}$, then $5A - 3B + 2C =$
Question 62 :
IF A=$\displaystyle \begin{vmatrix} 5 & x \\ y & 6 \end{vmatrix} $ B=$\displaystyle \begin{vmatrix} -4 & y \\ -4 & -5 \end{vmatrix} $and A+B=I then the values of x and y respectively are
Question 64 :
If order of $A+B$ is $n \times n$, then the order of $AB$ is
Question 65 :
If a matrix has $13$ elements, then the possible<br>dimensions (orders) of the matrix are
Question 67 :
Let $A = \begin{bmatrix} 1 & 0 & 0\\ 2 & 1 & 0\\ 3 & 2 & 1\end{bmatrix}$. If $u_1$ and $u_2$ are column matrices such that $Au_1 = \begin{bmatrix}1\\0\\0\end{bmatrix}$ and $Au_2 = \begin{bmatrix}0\\1\\0\end{bmatrix}$ then $u_1 + u_2$ is equal to
Question 68 :
The element in the second row and third column of the matrix $\displaystyle \begin{bmatrix}4 &5  &-6 \\3  &-4  &3 \\2  &1  &0 \end{bmatrix}$ is:
Question 69 :
If $A = \begin{bmatrix}2 & 3 & 4 \\ -3 & 4 & 8\end{bmatrix}$ and $B = \begin{bmatrix}-1 & 4 & 7 \\ -3 & -2 & 5\end{bmatrix}$, Then $\quad A+B = \begin{bmatrix}1 & a & b \\ c & 2 & 13\end{bmatrix}$<br/>Find the value of $a+b+c=$
Question 70 :
If $ A= \begin{bmatrix} 1 & 2\end{bmatrix}, B=\begin{bmatrix} 3 & 4\end{bmatrix}$ then $A+B=$
Question 71 :
The matrix $\begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}$ is the matrix reflection in the line
Question 73 :
If $A=\begin{bmatrix} { a }^{ 2 } & ab & ac \\ ab & { b }^{ 2 } & bc \\ ac & bc & { c }^{ 2 } \end{bmatrix}$ and ${a}^{2}+{b}^{2}+{c}^{2}=1$ then ${A}^{2}=$
Question 76 :
If $m  \begin{bmatrix} -3 & 4  \end{bmatrix}+n\begin{bmatrix} 4 & -3  \end{bmatrix}=\begin{bmatrix} 10 & -11  \end{bmatrix}$, then $ 3m\ + 7n=$<br/>
Question 77 :
If A=$\displaystyle \begin{vmatrix} 0 & 1 \\ 2 & 4 \end{vmatrix} $, B=$\displaystyle \begin{vmatrix} -1 & 1 \\ 2 & 2 \end{vmatrix} $,<br>C=$\displaystyle \begin{vmatrix} 1 & 0 \\ 1 & 0 \end{vmatrix} $, then 2A+3B-C=<br>
Question 78 :
A $2 \times 2$ matrix whose elements $\displaystyle a_{ij}$ are given by $\displaystyle a_{ij}=i-j$ is
Question 79 :
If a matrix has $m$ rows and $n$ columns then its order is
Question 80 : <p>The possibility for the formation of rectangular matrices in the matrix algebra are</p>
Question 81 :
Let $A  \begin{bmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{bmatrix}  $. If $u_{1}$ and $ u_{2}$ are column matrix such that $ A{ u }_{ 1 } \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}  $ and $ A{ u }_{ 2 } \begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix}  $ then $u_{1}+ u_{2}$ is equal to
Question 82 :
The possible number of different orders that a matrix can have when it has 24 elements,is
Question 83 :
If $\left[\begin{array}{ll}<br/>x+3 & 2y+x\\<br/>z-1 & 4a-z<br/>\end{array}\right]=\left[\begin{array}{ll}<br/>0 & -7\\<br/>3 & 2a<br/>\end{array}\right],$ then $(x+y+z+a)$ is:
Question 84 :
If $A$ and $B$ are non - zero square matrices of the same order such that $AB = 0$, then
Question 85 : <table class="wysiwyg-table"><tbody><tr><td></td><td>Day 1</td><td>Day 2</td><td>Day 3</td></tr><tr><td>Model X</td><td>$20$</td><td>$18$</td><td>$3$</td></tr><tr><td>Model Y</td><td>$16$</td><td>$5$</td><td>$8$</td></tr><tr><td>Model Z</td><td>$19$</td><td>$11$</td><td>$10$</td></tr></tbody></table>The table above shows the number of TV sets that were sold during a three-day sale. The prices of models $X, Y$ and $Z$ are $ $99$, $ $199$, and $ $299$, respectively. Which of the following matrix representations gives the total income, in dollars, received from the sale of the TV sets for each of the three days?
Question 86 :
Given $\displaystyle A=\begin{bmatrix}2 &-1 \\2  &0 \end{bmatrix},B=\begin{bmatrix}-3 &2 \\4  &0 \end{bmatrix}\:and\:C=\begin{bmatrix}2 &0 \\0  &2 \end{bmatrix},$ find the matrix $X$ such that<br/> $A+X=2B+C$
Question 87 :
If $A=\begin{bmatrix}1 & 0\\ -1 & 7\end{bmatrix}$ and $A^2=8A+KI_2$, then $K$ is equal to
Question 88 :
If $A=\begin{bmatrix} \sin ^{ 2 }{ \alpha  }  & \sec ^{ 2 }{ \alpha  }  \\ co\sec ^{ 2 }{ \alpha  }  & 1/2 \end{bmatrix}$ and $B=\begin{bmatrix} \cos ^{ 2 }{ \alpha  }  & -\tan ^{ 2 }{ \alpha  }  \\ -\cot ^{ 2 }{ \alpha  }  & 1/2 \end{bmatrix}$, then $A+B$ is equal to
Question 89 :
Given the equality of the following determinants. Find the value of $(a+b)$.<br>$\begin{vmatrix} 4 & 3\\ 6 & a\end{vmatrix} = \begin{vmatrix} 6 & b \\ 4 & 5\end{vmatrix}$<br><br>
Question 90 :
If A is square matrix such that $A (Adj A)=\left( \begin{matrix} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \end{matrix} \right) $ then det (Adj A)=
Question 91 :
If A and B are square matrices of order n x n such that ${ A }^{ 2 }-{ B }^{ 2 }=\left( A-B \right) \left( A+B \right) ,$ then of the following will always be true?
Question 92 :
The total number of matrices formed with the help of $6$ different numbers are
Question 93 :
For $3\times 3$ matrices $A$ and $B$, if $\left| B \right| =1$ and $A=2B$ then find $\left| A \right|$.
Question 94 :
Let $a$ denote the element of the ${i^{th}}$ row and ${j^{th}}$ column in a $3 \times 3$ matrix and let ${a_{ij}} = \, - {a_{ji}}$ for every i and j then this matrix is an -
Question 95 :
A matrix has $16$ elements Which of the following can be the order of the matrix?
Question 96 :
If $A$ and $B$ are matrices of order $3\times 2$ and $C$ is of order $2\times 3$, then which of the following matrices is not defined-
Question 97 :
$B=A+A^{2}+A^{3}+A^{4}$ <br/>If order of $A$ is $3$ then order of $B$ is 
Question 98 :
Unit matrix is a diagonal matrix in which all the diagonal elements are unity. Unit matrix of order 'n' is denoted by $I_n(or \ I)$ i.e. $A = [a_{ij}]_n$ is a  unit matrix when $a_{ij} = 0$ for $i \neq j \ and \ a_{ij} = 1$
Question 99 :
If $A=\begin{bmatrix} 4 & 1 & 0 \\ 1 & -2 & 2 \end{bmatrix},B=\begin{bmatrix} 2 & 0 & -1 \\ 3 & 1 & 4 \end{bmatrix},C=\begin{bmatrix} 1 \\ 2 \\ -1 \end{bmatrix}$ and $(3B-2A)C+2X=0$ then $X=$
Question 100 :
If $A =\displaystyle \begin{bmatrix} -1 & 0 &0  \\ 0 & x & 0 \\ 0 & 0 & m \end{bmatrix}$ is a scalar matrix then $x+m=$
Question 101 :
If $\begin{bmatrix} x & 0 \\ 1 & y \end{bmatrix}-\begin{bmatrix} 2 & -4 \\ -3 & -4 \end{bmatrix}=\begin{bmatrix} 3 & 5 \\ 6 & 3 \end{bmatrix}-\begin{bmatrix} 2 & 1 \\ 2 & 1 \end{bmatrix}$ then x=?,y=?
Question 102 :
If $A = \begin{bmatrix} 2 & 3\\ 6 & x \end{bmatrix}, B = \begin{bmatrix} 2 & 3\\ p & 2 \end{bmatrix}$ and A = B, then p and x are<br/>
Question 103 :
The order of [x, y, z]$\begin{bmatrix}a & h & g\\ h & b & f\\ g & f & c\end{bmatrix}$ <br> $\begin{bmatrix}x\\ y \\z \end{bmatrix}$ is
Question 105 :
The number of elements that a square matrix of order $n$ has below its leading diagonal is
Question 106 :
If $A = \bigl(\begin{bmatrix}7 &2 \\ 1 & 3\end{bmatrix}\bigr)$ and $A + B = \bigl(\begin{bmatrix} -1& 0\\ 2 & -4\end{bmatrix}\bigr)$, then the matrix B =<br/>
Question 107 :
A is of order $m \times n$ and B is of order $p \times q$, addition of A and B is possible only if<br>
Question 108 :
Out of the following matrices, choose that matrix which is a scalar matrix.
Question 109 :
If $\begin{vmatrix} x-4 & 2x & 2x \\ 2x & x-4 & 2x \\ 2x & 2x & x-4 \end{vmatrix}$ = $(A+Bx)(x-A)^2$,<br>then the ordered pair $(A , B)$ is equal to:
Question 110 :
If the number of elements in a matrix is $60$ then how many different order of matrix are possible 
Question 111 :
When a row matrix is multiplied by a column matrix both having the same number of elements, the resulting matrix formed is a ___?
Question 112 :
Let $C_k =$ $^nC_k$ for $0\leq k\leq n$ and<br>$A_k=\begin{bmatrix}C_{k-1}^2&0 \\0 &C_k^2 \end{bmatrix}$ for $k\geq 1$, and $A_1+A_2+ ... + A_n=\begin{bmatrix}k_1 &0 \\0 &k_2\end{bmatrix}$, then<br>
Question 113 :
$\left[ \begin{matrix} x \\ 3 \end{matrix}\begin{matrix} 6 \\ 2x \end{matrix} \right]$ is a singular matrix, then $x$ is equal to
Question 114 :
If $A = \dfrac {1}{\pi} \begin{bmatrix}\sin^{-1}(\pi x) & \tan^{-1} \left (\dfrac {\pi}{\pi}\right )\\ \sin^{-1} \left (\dfrac {x}{\pi}\right ) &\cot^{-1} (\pi x)\end{bmatrix}, B =\dfrac {1}{\pi} \begin{bmatrix}-\cos^{-1}(\pi x) &\tan^{-1} \left (\dfrac {x}{\pi}\right ) \\ \sin^{-1} \left (\dfrac {x}{\pi}\right ) & -\tan^{-1} (\pi x)\end{bmatrix}$, then $A - B$ is equal to<br/>
Question 115 :
Consider $A$ and $B$ two square matrices of same order. Select the correct alternative.
