Question 1 :
Given $A= \begin{bmatrix}  3&4  \\ 4&-3 \end{bmatrix}$ and $B = \begin{bmatrix} 24 \\ 7\end{bmatrix},$ find the matrix $X$<b> </b>such that $AX=B$.
Question 2 :
Find the output order for the following matrix multiplication $A_{4 \times 2}\times B_{2\times4}$?<br/>
Question 3 :
$[A]_{n\times m}, [B]_{m\times m},$ are the two matrices. If multiplication AB exist, then<br/>
Question 4 :
If $A=\begin{bmatrix} 1 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 1 \end{bmatrix}$ then $A^ {2}$ is equal to
Question 5 :
If $A = \begin{bmatrix}3 & 1 \\ -1 & 2\end{bmatrix}$, Then $A^2$ =
Question 6 :
What is $\begin{bmatrix} x & y & z \end{bmatrix} \begin{bmatrix} a& h & g\\ h & b & f\\ g & f & c\end{bmatrix}$ equal to?
Question 7 :
If $A = \left[ {\begin{array}{*{20}{c}}  2&{ - 3} \\   { - 4}&1 \end{array}} \right]$, then $\left[ {3{A^2} + 12A} \right]$ is equal to 
Question 9 :
If $A$ is matrix of order $\displaystyle m\times n$ and $B$ is a matrix of order $\displaystyle n\times p,$ then the order of $AB$ is 
Question 10 :
What is the output order for the following matrix multiplication $A_{2 \times 1}\times B_{1\times 2}$?<br/>
Question 11 :
If $A$ and $B$ are two matrices such that $A + B$ and $AB$ are both defined, then 
Question 12 :
If $A=\left[\begin{array}{lll}<br/>1 & -2 & 3\\<br/>-4 & 2 & 5<br/>\end{array}\right]$ and $B=\left[\begin{array}{ll}<br/>2 & 3\\<br/>4 & 5\\<br/>2 & 1<br/>\end{array}\right],$ then <br/>
Question 13 :
If $A = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}$, $B = \begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix}$, then $BA =$
Question 14 :
If a matrix $A$ is of order $3\times 4$ and a matrix $B$ is of order $4\times 3$, then the order of $BA$ is
Question 15 :
If $\begin{bmatrix}3 & -1 \\ 2 & 5\end{bmatrix}\begin{bmatrix}x \\ y \end{bmatrix} = \begin{bmatrix}4 \\ -3\end{bmatrix},$ find $x$ and $y$
Question 16 :
If $\begin{bmatrix} 1 & 2 & 3   \end{bmatrix}   B=\begin{bmatrix}  3 & 4   \end{bmatrix}$, then the order of the matrix $B$ is
Question 17 :
Consider the following statements:<br>1. The product of two non-zero matrices can never be identity matrix.<br>2. The product of two non-zero matrices can never be zero matrix.<br>Which of the above statements is/are correct?
Question 18 :
If $A=\begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$ and $B=\begin{bmatrix} 1 & 3 & 2 \\ 2 & 3 & 4 \end{bmatrix}$, then $AB$ equal to 
Question 19 :
If $A$ is any matrix, then the product $AA$ is defined only when A is a matrix of order $m \times n$ where : <span><br/></span>
Question 20 :
The order of $[\mathrm{x} \space \mathrm{y} \space\mathrm{z}] \left[\begin{array}{lll}<br/>\mathrm{a} & \mathrm{h} & \mathrm{g}\\<br/>\mathrm{h} & \mathrm{b} & \mathrm{f}\\<br/>\mathrm{g} & \mathrm{f} & \mathrm{c}<br/>\end{array}\right]\left[\begin{array}{l}<br/>\mathrm{x}\\<br/>\mathrm{y}\\<br/>\mathrm{z}<br/>\end{array}\right]$ is<br/>
Question 21 :
If $A=\begin{bmatrix} -1 & 0 \\ 0 & 2 \end{bmatrix} $, then $ A^{3}-A^{2}=$
Question 23 :
Given $A= \begin{bmatrix}  3&4  \\ 4&-3 \end{bmatrix}$ and $B = \begin{bmatrix} 24 \\ 7\end{bmatrix},$ find the matrix $X$<b> </b>such that $AX=B$.
Question 24 :
If $A$ is of order $3\times 4$ and $B$ is of order $4\times 3$ , then the order of $BA$ is :
Question 25 :
If $A=\begin{bmatrix} 2 & x-3 & x-2 \\ 3 & -2 & -1 \\ 4 & -1 & -5 \end{bmatrix}$ is a symmetric matrices then $x=$
Question 26 :
If the matrices $A=\begin{bmatrix}2 & 1 & 3 \\4 & 1 & 0\end{bmatrix}$ and $B=\begin{bmatrix}1 & -1\\ 0 & 2 \\5 & 0\end{bmatrix}$, then AB will be
Question 27 :
If $A=\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$, then $A^{4}=$<span><br/></span>
Question 28 :
If $A = \begin{bmatrix} 2& 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 2\end{bmatrix}$, then $A^6 =$
Question 29 :
IF $A=\begin{bmatrix} -1 & 0 & 2 \\ 3 & 1 & 2 \end{bmatrix}$ and $B=\begin{bmatrix} -1 & 5 \\ 2 & 7 \\ 3 & 10 \end{bmatrix},$ then
Question 30 :
If $A=[1\ \  2\ \  3\ \  4]$ and $AB = [3 \ \ 4\ \  -1],$ then the order of<br/>matrix $B$ is 
Question 31 :
If $A= \begin{bmatrix}<br/>1 & 2 & 3\\ <br/>4 & 5 & 6<br/>\end{bmatrix}$ and $B= \begin{bmatrix}<br/>1\\ <br/>0\\ <br/><br/>5\end{bmatrix},$ then $AB = $
Question 32 :
If $A = \begin{bmatrix}a & b\end{bmatrix},\space B = \begin{bmatrix}-b & -a \end{bmatrix}$ and $C = \begin{bmatrix}a \\ -a\end{bmatrix}$, then the correct statement is
Question 33 :
If $A=\begin{bmatrix} 1&2 \\ 2 &3\\3 & 4\end{bmatrix}$ and $B=\begin{bmatrix} 1 &  2\\ 2 &  1\end{bmatrix},$ then which one of the following is correct?
Question 34 :
lIf $\mathrm{A} =\left[\begin{array}{ll}<br/>a & 0\\<br/>a & 0<br/>\end{array}\right],\ \mathrm{B}=\left[\begin{array}{ll}<br/>0 & 0\\<br/>b & b<br/>\end{array}\right],$ then $\mathrm{A}\mathrm{B}=$ <br/>
Question 35 :
If $\displaystyle \begin{bmatrix} 1&2&3\end{bmatrix} A=\begin{bmatrix} 4&5 \end{bmatrix}, $ then what is the order of matrix $A$?
Question 36 :
If $\mathrm{A}=\left[\begin{array}{lll}<br/>1 & -3 & -4\\<br/>-1 & 3 & 4\\<br/>1 & -3 & -4<br/>\end{array}\right]$, then $\mathrm{A}^{2}=$<br/>
Question 37 :
If $[2\ 3\ 4] \begin{bmatrix}1 & x &3 \\ 2 & 4 & 5\\ 3 & 2 &x \end{bmatrix} \begin{bmatrix} x\\ 2 \\ 0 \end{bmatrix} = 0$, then $x =$ ________.<br>
Question 38 :
If $A=\displaystyle \left[ \begin{matrix} 1 & -6 & 2 \\ 0 & -1 & 5 \end{matrix} \right] $ and $\displaystyle B=\left[ \begin{matrix} 2 \\ 1 \end{matrix} \right] $, then $AB$ equals
Question 39 :
iF $A=\begin{bmatrix} 1& -1\\ -1& 1\end{bmatrix}$, then the expression $A^3-2A^2$ is
