Question 1 :
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 2 :
IF A=$\displaystyle \begin{vmatrix} 1 & 0 \\ 1 & 0 \end{vmatrix} $ And B=$\displaystyle \begin{vmatrix} 1 & 0 \\ 0 & 1 \end{vmatrix} $ then A+B=
Question 3 :
If order of $A+B$ is $n \times n$, then the order of $AB$ is
Question 4 :
If matrix $A$ is of order $p\times q$ and matrix $B$ is of order $r\times s$ then $A-B$ will exist if-
Question 6 :
If $m[-3\ \ \ 4]+n[4\ \ \ -3]=[10\ \ \ -11]$ then $3m+7n=$
Question 7 :
The number of all possible matrices of order $3 \times 3$ with each entry $0$ or $1$ is:
Question 8 :
If $ A= \begin{bmatrix} 1 & 2\end{bmatrix}, B=\begin{bmatrix} 3 & 4\end{bmatrix}$ then $A+B=$
Question 9 :
If $\displaystyle A=\begin{bmatrix}x &y \\z  &w \end{bmatrix},B=\begin{bmatrix}x &-y \\-z  &w \end{bmatrix}$ and $C=\begin{bmatrix}-2x &0 \\0  &-2w \end{bmatrix},$ then $A+B+C$ is a:
Question 10 :
If $A= \begin{bmatrix} 1 & 2 & 3\end{bmatrix}$, then order is
Question 11 :
If the matrix $\begin{bmatrix} 1 & 3 & \lambda +2 \\ 2 & 4 & 8 \\ 3 & 5 & 10 \end{bmatrix}$ is singular, then $\lambda=$
Question 12 :
The order of a matrix $\begin{bmatrix} 2& 5& 7\end{bmatrix} $ is 
Question 13 :
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 14 :
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 15 :
If for a matrix $\displaystyle A,{ A }+I=O$, where $I$ is an identity matrix, then $A$ equals
Question 16 :
If a matrix has $m$ rows and $n$ columns then its order is
Question 17 :
Suppose $A$ and $B$ are two square matrices of same order. If $A,B$ are symmetric matrices and $AB=BA$ then $AB$ is
Question 18 :
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 19 :
A $2 \times 2$ matrix whose elements $\displaystyle a_{ij}$ are given by $\displaystyle a_{ij}=i-j$ is
Question 20 :
If $\begin{bmatrix}r+4 & 6 \\3 & 3\end{bmatrix} = \begin{bmatrix} 5 & r+5 \\ r+2 & 4 \end{bmatrix}$ then $r= $ <br/>
Question 21 :
The order the matrix is $ \begin{bmatrix}2 & 3 & 4 \\ 9 & 8 & 7 \end{bmatrix}$ is <br/>
Question 22 :
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    $A \cdot \left[ \begin{array} { c c } { 1 } & { 2 } \\ { 0 } & { 3 } \end{array} \right]$is equal to
Question 23 :
The order of $\begin{bmatrix}x & y & z\end{bmatrix}\begin{bmatrix}a & h & g \\ h & b & f \\ g & f & c\end{bmatrix}\begin{bmatrix}x\\ y \\z\end{bmatrix}$ is
Question 24 :
If $\displaystyle A = \begin{bmatrix} 1 & -2 & 4 \\ 2 & 3 & 2 \\ 3 & 1 & 5 \end{bmatrix}$ and $\displaystyle B = \begin{bmatrix} 0 & -2 & 4 \\ 1 & 3 & 2 \\ -1 & 1 & 5 \end{bmatrix}$, then $A + B$ is
Question 25 :
The Inverse of a square matrix, if it exist is unique.
Question 27 :
<b>If $A$ is a square of order $3$, then</b> $\left| Adj\left( Adj{ A }^{ 2 } \right)\right| =$
Question 28 :
${a}^{-1}+{b}^{-1}+{c}^{-1}=0$ 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 29 :
If P=$\displaystyle  \begin{bmatrix} 4 & 3 &2   \end{bmatrix}  $ and Q=$\displaystyle  \begin{bmatrix} -1 & 2 &3   \end{bmatrix}  $ then P-Q=
Question 30 :
$\displaystyle { A=\left[ { a }_{ ij } \right] }_{ m\times n}$ is a square matrix , if
Question 31 :
A square matrix A has 9 elements. What is the possible order of A?
Question 32 :
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 33 :
If $A= [ 1 \ 2\  3 ]$, then the set of elements of A is
Question 34 :
If order of a matrix is $3 \times 3$, then it is a
Question 36 :
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 37 :
If $A$ and $B$ are square matrices such that $AB = I$ and $BA = I$, then $B$ is<br/>
Question 38 :
If $\displaystyle A=\left [ a_{ij} \right ]_{m\times\:n'}B=\left [ b_{ij} \right ]_{m\times\:n'}$ then the element $\displaystyle C_{23}$ of the matrix $C=A+B$, is:
Question 39 :
If A+$\displaystyle \begin{vmatrix} 4 & 2 \\ 1 & 3 \end{vmatrix} $=$\displaystyle \begin{vmatrix} 6 & 9 \\ 1 & 4 \end{vmatrix} $ then A=
Question 40 :
The number of possible orders of a matrix containing $24$ elements are:
Question 41 :
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 43 :
Construct the matrix of order $3 \times 2$ whose elements are given by $a_{ij} = 2i - j$
Question 44 :
If order of matrix $A$ is $4\times3$ and order of matrix $B$ is $3\times5$ then order of matrix $B'A'$ is:
Question 45 : <p>The possibility for the formation of rectangular matrices in the matrix algebra are</p>
Question 46 :
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 47 :
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 49 :
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 50 :
If $2A-\begin{bmatrix} 1 & 2 \\ 7 & 4 \end{bmatrix}=\begin{bmatrix} 3 & 0 \\ 0 & -2 \end{bmatrix}$, then $A$ is equal to-
