Question 1 :
A <b>matrix</b> consisting of a single <b>column</b> of m elements is know as
Question 2 :
<div>If $\displaystyle \begin{vmatrix} a & b &0\\ 0 & a & b\\b&a&0\end{vmatrix}= 0$, then the order is:</div>
Question 3 :
If order of matrix $A$ is $4\times3$ and order of matrix $B$ is $3\times5$ then order of matrix $B'A'$ is:
Question 5 :
If order of $A+B$ is $n \times n$, then the order of $AB$ is
Question 6 :
A $2 \times 2$ matrix whose elements $\displaystyle a_{ij}$ are given by $\displaystyle a_{ij}=i-j$ is
Question 7 :
${a}^{-1}+{b}^{-1}+{c}^{-1}=0$ such that $\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix}=\triangle$  then the value of $\triangle$  is
Question 8 :
If $A = \begin{bmatrix}1\end{bmatrix}$, then the order of the matrix is
Question 9 :
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 10 :
Construct a $2\times3$ matrix $A = [a_{ij}]$ whose elements are given by $a_{ij} = 2(i - j)$
Question 11 :
If $\begin{bmatrix}4 &-3 \\ 2 & 16\end{bmatrix}$ = $\begin{bmatrix}4 &-3 \\ 2 & 2^t\end{bmatrix}$, then t = _______
Question 12 :
A square matrix $\left[ { a }_{ ij } \right] $ such that ${ a }_{ ij }=0$ for $i\ne j$ and ${ a }_{ ij }=k$ where $k$ is a constant for $i=j$ is called:
Question 13 :
<span>If $A=\displaystyle \left[ \begin{matrix} 1 &2 \\ 3& 4 \end{matrix} \right] $, then which of the following is not an element of $A$?</span>
Question 16 :
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 17 :
The number of possible orders of a matrix containing $24$ elements are:
Question 18 :
The number of all possible matrices of order $3 \times 3$ with each entry $0$ or $1$ is:
Question 19 :
The Inverse of a square matrix, if it exist is unique.
Question 20 :
If the matrix $\begin{bmatrix} 1 & 3 & \lambda +2 \\ 2 & 4 & 8 \\ 3 & 5 & 10 \end{bmatrix}$ is singular, then $\lambda=$
Question 21 :
If a matrix has $13$ elements, then the possible<br>dimensions (orders) of the matrix are
Question 23 :
If order of a matrix is $3 \times 3$, then it is a
Question 25 :
If $m[-3\ \ \ 4]+n[4\ \ \ -3]=[10\ \ \ -11]$ then $3m+7n=$
Question 26 :
The matrix $\begin{bmatrix}0 & 1 \\ 1 & 0 \end{bmatrix}$ is the matrix reflection in the line
Question 27 :
$\displaystyle { A=\left[ { a }_{ ij } \right] }_{ m\times n}$ is a square matrix , if
Question 28 :
If $A=\begin{bmatrix}5 & 2\\ 7 & 4\end{bmatrix}$ is a $2\times 2$ matrix, then $a_{12}$=
Question 29 :
If $A= [ 1 \ 2\  3 ]$, then the set of elements of A is
Question 30 :
For any square matrix $A=[{a}_{ij}],{a}_{ij}=0$, when $i\ne j$, then $A$ is
Question 31 :
<b>If $A$ is a square of order $3$, then</b> $\left| Adj\left( Adj{ A }^{ 2 } \right)\right| =$
Question 32 :
Given that $\displaystyle M=\begin{bmatrix}3 &-2 \\-4  &0 \end{bmatrix}\:and\:N=\begin{bmatrix}-2 &2 \\5  &0 \end{bmatrix}$<span>, then $M+N$ is a </span>
Question 33 :
<p>The possibility for the formation of rectangular matrices in the matrix algebra are</p>
Question 34 :
The order of a matrix $\begin{bmatrix} 2& 5& 7\end{bmatrix} $ is 
Question 35 :
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 36 :
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 37 :
Let  $A$  be a matrix such that  $A \cdot \left[ \begin{array} { c c } { 1 } & { 2 } \\ { 0 } & { 3 } \end{array} \right]$  is a scalar matrix and  $| 3 A | = 108 .$  Then  <span>  $A \cdot \left[ \begin{array} { c c } { 1 } & { 2 } \\ { 0 } & { 3 } \end{array} \right]$is equal to</span>
Question 38 :
A matrix having $m$ rows and $n$ columns with $m=n$ is said to be a 
Question 39 :
If $A= \begin{bmatrix} 1 & 2 & 3\end{bmatrix}$, then order is
Question 40 :
A matrix having $m$ rows and $n$ columns with $m  \displaystyle \neq   n$ is said to be a
Question 41 :
Suppose $A$ and $B$ are two square matrices of same order. If $A,B$ are symmetric matrices and $AB=BA$ then $AB$ is
Question 42 :
The number of different possible orders of matrices having 18 identical elements is
Question 43 :
The order of the matrix $\displaystyle \begin{bmatrix}-1\\3 \\4 <br>\end{bmatrix}$ is :
Question 44 :
If every row of a matrix $A$ contains $p$ elements and its column contains $q$ elements, then the order of $A$ is
Question 45 :
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 48 :
If $A$ and $B$ are square matrices such that $AB = I$ and $BA = I$, then $B$ is<br/>
Question 51 :
$A=\begin{bmatrix} 1 & 2 & 3 \\ 1 & 2 & 3 \\ -1 & -2 & -3 \end{bmatrix}$, then A is a nilpotent matrix of index
Question 52 :
If $A, B$ are square matrices of order $3$, A is non-singular and $AB = O$, then $B$ is a
Question 53 :
If $\bigl(\begin{smallmatrix} 3x+ 7& 5 \\ y + 1 & 2 - 3x\end{smallmatrix}\bigr) = \bigl(\begin{smallmatrix}1 & y - 2 \\ 8 & 8\end{smallmatrix}\bigr)$ then the values of x and y respectively are<br>
Question 55 :
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 56 :
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 57 :
If A is a square matrix of order n, then adj (adj A ) is equal to
Question 58 :
If $A$ is a square matrix of order $n\times n$, then adj(adj A) is equal to
Question 59 :
If $A=\begin{vmatrix} \begin{matrix} -2 \\ 4 \end{matrix} \\ 5 \end{vmatrix},\,B=\begin{vmatrix} \begin{matrix} 1 & 3 & -6 \end{matrix} \end{vmatrix}$, State whether ist is true or false ${(AB)}^{1}={B}^{1}\,{A}^{1}$
Question 60 :
Given $A=\left[ \begin{matrix} 1 & 3 \\ 2 & 2 \end{matrix} \right] $, $I=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right] $ . If $A-\lambda I$ is a singular matrix then 
Question 61 :
<div>Find the value of </div><div><br/></div>$A=\begin{vmatrix} 1 & 5 & 7 \\ 5 & 25 & 35 \\ 12 & 20 & 24 \end{vmatrix}$<br/>
Question 62 :
If the square of the matrix $\begin{bmatrix} a & b \\ a & -a \end{bmatrix}$ is the unit matrix, then $b$ is equal to
Question 63 :
The minimum number of zero's in an upper triangular matrix of order $n\times n$ is-
Question 64 :
Matrix $A = [a_{ij}]_{m \times n}$ is a square matrix if<br>
Question 65 :
If $A= [a_{ij}]_{2 \times 2}$ and $a_{ij} = i + j$, then A = <br>
Question 67 :
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 68 :
If a,b,c are distinct and $\left| \begin{matrix} a & { a }^{ 2 } & { a }^{ 3 }-1 \\ b & { b }^{ 2 } & { b }^{ 3 }-1 \\ c & { c }^{ 2 } & { c }^{ 3 }-1 \end{matrix} \right| =0$ then
Question 69 :
If $A$ and $B$ are two matrices of order $3\times m$ and $3\times n$ respectively and $m = n$, then the order of $5A - 2B$ is
Question 70 :
If the order of matrices $A$ and $B$ are $3 \times 2$ and $2 \times 1 $ respectively, then find the order of matrix (if possible) $AB$
Question 72 :
The order of [x, y, z] $\begin{bmatrix}a & h & g\\ h & b & f\\ g & f & c\end{bmatrix}$ $\begin{bmatrix}x\\ y \\z \end{bmatrix}$ is
Question 73 :
Matrix $A= \begin{bmatrix}1& 3 & 3 \\ 2 & 4 & 10 \\ 3 & 8 & 4\end{bmatrix}$ is similar to
Question 74 :
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 75 :
If A and B are square matrices of order 'n' such that $A^2-B^2=(A-B)(A+B)$, then which of the following will be true?<br>
Question 76 :
If $A$ is a square matrix such that $A^{2} = I$, then $(A - I)^{3} + (A + I)^{3} - 7A$ is equal to
Question 78 :
The matrix $A=\begin{bmatrix} 0 & 0 & 5 \\ 0 & 5 & 0 \\ 5 & 0 & 0 \end{bmatrix}$ is a
Question 79 :
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 81 :
Assertion: The possible dimension of a matrix consisting $27$ elements is $4.$
Reason: The number of ways of expressing $27$ as a product of two positive integers is $4.$
Question 83 :
If A = $ \begin{bmatrix} \alpha & 0 \\ 1 & 1\end{bmatrix}$ , B = $ \begin{bmatrix} 1 & 0 \\ 5 & 1\end{bmatrix}$ whenever $A^2 \, = \, B$<br>then values of $\alpha$ is
Question 84 :
If A=$\displaystyle \left [ a_{ij} \right ]_{2\times 2}$ such that $\displaystyle a_{ij}=i-j+3$ then find $A$
Question 85 :
<div><span>$B=A+A^{2}+A^{3}+A^{4}$ </span><br/></div><div><span>If order of $A$ is $3$ then order of $B$ is </span></div>
Question 87 :
The matrix $P=\begin{bmatrix} 0 & 0 & 4 \\ 0 & 4 & 0 \\ 4 & 0 & 0 \end{bmatrix}$ is a
Question 88 :
If $A$ and $B$ are non - zero square matrices of the same order such that $AB = 0$, then
Question 89 :
If two square matrices $A$ and $B$ are of same order and, $Tr(A) = 3, Tr(B) = 5$ then $Tr(A+B) =$
Question 90 :
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 91 :
A matrix has $16$ elements Which of the following can be the order of the matrix?
Question 93 :
The restriction on $ n, k$ and $p$ so that $PY + WY$ will be defined are:<br>
Question 94 :
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 95 :
lf $\mathrm{A}=[\mathrm{a}_{\mathrm{i}\mathrm{j}}]$ is a scalar matrix of order  $n\times n$ such that $\mathrm{a}_{\mathrm{i}\mathrm{j}}=\mathrm{k}$ for all $\mathrm{i}=j$, then trace of $\mathrm{A}=$<br/>
Question 96 :
If A is $3 \times 4$ matrix and B is matrix such that A'B and BA' are both defined, then B is of the type.<br>
Question 98 :
If $A = \left[ \begin{array} { r r } { 2 } & { - 3 } \\ { - 4 } & { 1 } \end{array} \right] ,$ then adj $\left( 3 A ^ { 2 } + 12 A \right)$ is <span>equal to :</span>
Question 100 :
If $A$ is a square matrix of order $3$ such that $A^{2} + A + 4I = 0$, where $0$ is the zero matrix and $I$ is the unit matrix of order $3$, then
Question 101 :
Out of the following matrices, choose that matrix which is a scalar matrix.
Question 102 :
$\left[ \begin{matrix} x \\ 3 \end{matrix}\begin{matrix} 6 \\ 2x \end{matrix} \right]$ is a singular matrix, then $x$ is equal to
Question 103 :
Two rectangular matrices of order $n\times m$ and $m\times k$ are multiplied in the same order. The resulting matrix formed is a:
Question 104 :
Consider $A$ and $B$ two square matrices of same order. Select the correct alternative.
Question 105 :
If A = $\begin{bmatrix}1 & 2 \\ 3 & 4 \end{bmatrix}$, B = $\begin{bmatrix}2 & 3 \\ 4 & 5 \end{bmatrix}$, and 4A - 3B + C = 0, then C =
Question 106 :
<div>If $0\le\left[x\right]<2,\,-1\le\left[y\right]<1$ and $1\le\left[z\right]<3$ ( $\left[.\right]$ denotes the greatest integer function) then the maximum value of determinant</div><div>$\Delta=\left| \begin{matrix} \left[x\right]+1 & \left[y\right]  & \left[z\right] \\ \left[x\right] & \left[y\right]+1  & \left[z\right] \\ \left[x\right] & \left[y\right]  & \left[z\right]+1 \end{matrix} \right|$ is</div>
Question 107 :
If $A(\theta )=\begin{bmatrix} \cos \theta & -\sin \theta &0 \\\sin \theta &\cos \theta &0 \\0 &0 &0 \end{bmatrix}$, then $A(\theta )^3$ will be a null matrix if and only if<br>
Question 108 :
If the number of elements in a matrix is $60$ then how many different order of matrix are possible 
Question 109 :
When a row matrix is multiplied by a column matrix both having the same number of elements, the resulting matrix formed is a ___?
Question 110 :
$\displaystyle \begin{vmatrix} 1 & a & {a}^{2}-bc \\ 1 & b & {b}^{2}-ca \\ 1 & c & {c}^{2}-ab \end{vmatrix}$=?
Question 111 :
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 112 :
Assertion: If $D = diag [d_1, d_2, ...., d_n]$, then $D^{-1} = diag [d_1^{-1}, d_2^{-1} ..... , d_n^{-1}]$
Reason: If $D = diag [d_1, d_2, ...... d_n], $ then $D^n = diag [d_1^n, d_2^n ...... , d_n^n].$
Question 113 :
If $A$ is $2\times 3$ matrix and $AB$ is a $2\times 5$ matrix, then $B$ must be a
Question 114 :
If D$_1$ and D$_2$ are two 3 $\times$ 3 diagonal matrices, then which of the following is/are true?
Question 115 :
Let $A = \begin{bmatrix} -2 & 7 & \sqrt{ 3}  \\ 0 & 0 & -2 \\ 0 & 2 & 0 \end{bmatrix} $  and $A^4 = \lambda$. I, then $\lambda $ is