Question 1 :
A square matrix $(a_{ij})$ in which $a_{ij}=0$ for $i \neq j$ and $a_{ij}= k (constant)$ for $i=j$ is a<br/>
Question 2 :
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 3 :
If order of a matrix is $3 \times 3$, then it is a
Question 4 :
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 5 :
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 6 : <p>The possibility for the formation of rectangular matrices in the matrix algebra are</p>
Question 7 :
The number of possible orders of a matrix containing $24$ elements are:
Question 8 :
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 9 :
If $A$ and $B$ are square matrices such that $AB = I$ and $BA = I$, then $B$ is<br/>
Question 11 :
If order of $A+B$ is $n \times n$, then the order of $AB$ is
Question 12 :
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 13 :
If $ A= \begin{bmatrix} 1 & 2\end{bmatrix}, B=\begin{bmatrix} 3 & 4\end{bmatrix}$ then $A+B=$
Question 14 :
The order of a matrix $\begin{bmatrix} 2& 5& 7\end{bmatrix} $ is 
Question 15 :
If $\begin{bmatrix}r+4 & 6 \\3 & 3\end{bmatrix} = \begin{bmatrix} 5 & r+5 \\ r+2 & 4 \end{bmatrix}$ then $r= $ <br/>
Question 16 :
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 17 :
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 18 :
The number of all possible matrices of order $3 \times 3$ with each entry $0$ or $1$ is:
Question 19 :
If $m[-3\ \ \ 4]+n[4\ \ \ -3]=[10\ \ \ -11]$ then $3m+7n=$
Question 20 :
The matrix $\begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}$ is the matrix reflection in the line
Question 21 :
A square matrix A has 9 elements. What is the possible order of A?
Question 22 : 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 23 :
If a matrix has $m$ rows and $n$ columns then its order is
Question 24 :
If a matrix has $13$ elements, then the possible<br>dimensions (orders) of the matrix are
Question 25 :
If P=$\displaystyle  \begin{bmatrix} 4 & 3 &2   \end{bmatrix}  $ and Q=$\displaystyle  \begin{bmatrix} -1 & 2 &3   \end{bmatrix}  $ then P-Q=
Question 26 :
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 27 :
If $\displaystyle \begin{vmatrix} a & b &0\\ 0 & a & b\\b&a&0\end{vmatrix}= 0$, then the order is:
Question 28 :
If $2A+B=\begin{bmatrix} 6 & 4 \\ 6 & -11 \end{bmatrix}$ and $A-B=\begin{bmatrix} 0 & 2 \\ 6 & 2 \end{bmatrix}$, then $A=$
Question 29 :
The order the matrix is $ \begin{bmatrix}2 & 3 & 4 \\ 9 & 8 & 7 \end{bmatrix}$ is <br/>
Question 30 :
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 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 33 :
The number of different possible orders of matrices having 18 identical elements is
Question 34 :
If $A= [ 1 \ 2\  3 ]$, then the set of elements of A is
Question 36 :
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 37 :
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 38 :
Construct the matrix of order $3 \times 2$ whose elements are given by $a_{ij} = 2i - j$
Question 39 :
A $2 \times 2$ matrix whose elements $\displaystyle a_{ij}$ are given by $\displaystyle a_{ij}=i-j$ is
Question 40 :
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 41 :
If every row of a matrix $A$ contains $p$ elements and its column contains $q$ elements, then the order of $A$ is
Question 42 :
If $A = {\left( {{a_{ij}}} \right)_{2 \times 2}}$, where ${a_{ij}} = i + j$, then $A$ is equal to:<br/>
Question 44 :
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 45 :
The Inverse of a square matrix, if it exist is unique.
Question 46 :
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 47 :
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 48 :
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 49 :
If $A= \begin{bmatrix} 1 & 2 & 3\end{bmatrix}$, then order is
Question 50 :
Suppose $A$ and $B$ are two square matrices of same order. If $A,B$ are symmetric matrices and $AB=BA$ then $AB$ is
