Question 1 :
Assertion: The matrix $\begin{bmatrix} a & 0 & 0 & 0 \\ 0 & b & 0 & 0 \\ 0 & 0 & c & 0 \end{bmatrix}$ is a diagonal matrix
Reason: $A[{a}_{ij}]$ is a square matrix such that ${a}_{ij}=0$ for all $i\ne j$, then $A$ is called diagonal matrix
Question 2 :
If $A=\begin{bmatrix}1 & 0\\ -1 & 7\end{bmatrix}$ and $A^2=8A+KI_2$, then $K$ is equal to
Question 3 :
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 4 :
If $A = \left[ \begin{array} { r r } { 2 } & { - 3 } \\ { - 4 } & { 1 } \end{array} \right] ,$ then adj $\left( 3 A ^ { 2 } + 12 A \right)$ isequal to :
Question 5 :
If the matrices has 13 elements , then the possible dimension (order) it can have are
Question 6 :
If$\displaystyle a_{ij}=0\left ( i\neq j \right )$ and$\displaystyle a_{ij}=1\left ( i= j \right )$ then the matrix A=$\displaystyle \left [ a_{ij} \right ]_{n\times n}$ is a _____ matrix
Question 7 :
The order of the matrix $\displaystyle \left[ \begin{matrix} 1 &2 \\ 3& 4 \end{matrix} \right] $ is:
Question 9 :
Find $m$ and $p$:<br>$\begin{bmatrix} 2 & 3 \\ -1 & 4 \end{bmatrix}\begin{bmatrix} 0 & m \\ 3 & p \end{bmatrix}=\begin{bmatrix} 9 & 6 \\ 12 & 19 \end{bmatrix}$
Question 10 :
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 11 :
If $I = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix},\space J =\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}$ and $B = \begin{bmatrix}\cos\theta & \sin\theta \\ -\sin\theta & \cos\theta\end{bmatrix}$, then $B$ equals
Question 12 :
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 13 :
The possible number of different orders that a matrix can have when it has 24 elements,is
Question 14 :
If $A$ and $B$ are two matrices such that $A+B$ and $AB$ are both defined, then
Question 15 :
If $m\begin{bmatrix} -3 & 4 \end{bmatrix}+n\begin{bmatrix} 4 & -3 \end{bmatrix}=\begin{bmatrix} 10 & -11 \end{bmatrix}$ then $3m+7n=$
Question 16 :
If $A$ is a square matrix of order $n\times n$, then adj(adj A) is equal to
Question 17 :
If $A$ is a matrix of order $m\times n$ and $B$ is a matrix such that $AB'$ and $B'A$ are both defined, the order of the matrix $B$ is
Question 18 :
If $A$ is a square matrix such that $A^{2} = I$, then $(A - I)^{3} + (A + I)^{3} - 7A$ is equal to
Question 19 :
A matrix has $18$ elements. Find the number of possible orders of the matrix
Question 20 :
If $A+B=\begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix}$ and $A=\begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix}$, then matrix $B$ is
Question 21 :
The total number of matrices formed with the help of $6$ different numbers are
Question 23 :
If $A = \begin{bmatrix}2 & -1\\ 3 & 1\end{bmatrix}$ and $B = \begin{bmatrix}1 & 4\\ 7 & 2\end{bmatrix}$,  $3A - 2 B$ is
Question 24 :
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 25 :
If $A + 2B = \begin{bmatrix} 1 & 2 & 0\\  6 & -3 & 3\\ -5 & 3 & 1\end{bmatrix}$ and $2A - B =  \begin{bmatrix} 2 & -1 & 5\\  2 & -1 & 6\\  0 & 1 & 2\end{bmatrix}$, then $tr(A) - tr(B) =$
Question 27 :
If $A$ and $B$ are square matrices such that $B = -A^{-1} BA, \,$ then $\, (A + B)^2$ is equal to 
Question 28 :
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 29 :
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 30 :
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 31 :
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 32 :
If $3\begin{bmatrix} 4 & 2 \\ 1 & 3 \end{bmatrix}-2\begin{bmatrix} -2 & 1 \\ 3 & 2 \end{bmatrix}+\begin{bmatrix} x & -4 \\ 3 & y \end{bmatrix}=0$ then $\left(x,y\right)=$
Question 33 :
Given, matrix $\displaystyle A=\begin{bmatrix}3\\2 <br/>\end{bmatrix}\:and\:B=\begin{bmatrix}-2\\-1 <br/>\end{bmatrix},$ find the matrix X such that $X - A = B$
Question 34 :
If a matrix $P$ has $8$ elements then how many different values the order of the matrix can take?
Question 35 :
Find the value of <br/>$A=\begin{vmatrix} 1 & 5 & 7 \\ 5 & 25 & 35 \\ 12 & 20 & 24 \end{vmatrix}$<br/>
Question 36 :
If $\left[\begin{array}{ll}<br/>r+2 & 5\\<br/>-2 & r+1<br/>\end{array}\right]=\left[\begin{array}{lll}<br/>4 & y+3\\<br/>z & 3<br/>\end{array}\right]$, then<br/>
Question 37 :
If AB = 0, then for the matrices $A=\begin{bmatrix} { \cos }^{ 2 }\theta  & \cos\theta \sin\theta  \\ \cos\theta \sin\theta  & { \sin }^{ 2 }\theta  \end{bmatrix}\ and \ B=\begin{bmatrix} { \cos }^{ 2 }\phi  & \cos\phi \sin\phi  \\ \cos\phi \sin\phi  & { \sin }^{ 2 }\phi  \end{bmatrix}, \theta - \phi$ is
Question 38 :
The order of any matrix is $3\times  2$ then no. of element in the matrix?
Question 39 :
If the order of a matrix is $\displaystyle 20\times 5$ then the number of elements in the matrix is _____
Question 40 :
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 41 :
If $\begin{bmatrix} i&0 \\3 &-i \end{bmatrix}+X=\begin{bmatrix} i&2 \\3 &4+i\end{bmatrix} - X$, then $X$ is equal to<br/>
Question 42 :
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 43 :
The matrix A satisfies the matrix equation if $A=\begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix}$<br/>
Question 44 :
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 45 :
If $A =\displaystyle \begin{bmatrix} -1 & 0 &0  \\ 0 & x & 0 \\ 0 & 0 & m \end{bmatrix}$ is a scalar matrix then $x+m=$
Question 46 :
For $3\times 3$ matrices $A$ and $B$, if $\left| B \right| =1$ and $A=2B$ then find $\left| A \right|$.
Question 47 :
If $A=\dfrac { 1 }{ \pi } \begin{bmatrix} \sin ^{ -1 }{ \left( x\pi \right) } & \tan ^{ -1 }{ \left( \dfrac { x }{ \pi } \right) } \\ \sin ^{ -1 }{ \left( \dfrac { x }{ \pi } \right) } & \cot ^{ -1 }{ \left( \pi x \right) } \end{bmatrix} B=\begin{bmatrix} -\cos ^{ -1 }{ \left( x\pi \right) } & \tan ^{ -1 }{ \left( \dfrac { x }{ \pi } \right) } \\ \sin ^{ -1 }{ \left( \dfrac { x }{ \pi } \right) } & -\tan ^{ -1 }{ \left( \pi x \right) } \end{bmatrix}$ then $A-B$ equal to
Question 48 :
$\begin{vmatrix} x+5 & x \\ x+9 & x-2 \end{vmatrix}=0$ then x=
Question 49 :
If $\displaystyle \begin{bmatrix}2 &-1 \\2  &0 \end{bmatrix}+2A=\begin{bmatrix}-3 &5 \\4  &3 \end{bmatrix},$ then the matrix A equals
Question 50 :
If $A$ is a matrix of order $m\times n$ and $B$ is a matrix such that $AB^{T}$ and $B^{T}A$ are both defined, then the order of matrix $B$ is
