Question 1 :
If $\displaystyle \:A= \left [ \begin{matrix}1 &2  &x \\0  &1  &0 \\0  &0  &1 \end{matrix} \right ]and \  B\left [ \begin{matrix}1 &-2  &y \\0  &1  &0 \\0  &0  &1 \end{matrix} \right ]$ and  $\displaystyle \:AB= I,$ then $x+y$ equals 

Question 2 :
If $\displaystyle A=\begin{bmatrix}0 &amp;c&#160; &amp;-b \\-c&#160; &amp;0&#160; &amp;a \\b&#160; &amp;-a&#160; &amp;0 \end{bmatrix}$&#160; and $\displaystyle B=\begin{bmatrix}a^{2} &amp;ab&#160; &amp;ac \\ab&#160; &amp;b^{2}&#160; &amp;bc \\ac&#160; &amp;bc&#160; &amp;c^{2} \end{bmatrix},$ then $AB=$<br/>

Question 4 :
If $A = \begin{bmatrix}&nbsp;0&amp; 1\\ 1&nbsp;&amp; 0\end{bmatrix}$, then $A^{2}$ is equal to ______<br>

Question 5 :
If $A=\begin{bmatrix} 2 &amp; -1 \\ -1 &amp; 2 \end{bmatrix}$ and $I$ is the unit matrix of order $2$, then $A^{2}$ equals&nbsp;

Question 6 :
If $A=\begin{bmatrix}x&amp;y&amp;z\end{bmatrix},$ $ B=\begin{bmatrix}a&amp;h&amp;g\\h&amp;b&amp;f\\g&amp;f&amp;c\end{bmatrix}, C=\begin{bmatrix}\alpha &amp; \beta &amp; \gamma \end{bmatrix}^{T}$ then $ABC$ is

Question 7 :
If $A = \begin{bmatrix}&nbsp;n&amp; 0 &amp; 0\\ 0&nbsp;&amp; n &amp; 0\\ 0&nbsp;&amp; 0 &amp; n\end{bmatrix}$ and $B =&nbsp;\begin{bmatrix}a_{1}&nbsp;&amp; a_{2} &amp; a_{3}\\ b_{1}&nbsp;&amp; b_{2} &amp; b_{3}\\ c_{1}&nbsp;&amp; c_{2} &amp; c_{3}\end{bmatrix}$, then $AB$ is equal to<br>

Question 8 :
If $A = \begin{bmatrix}&nbsp;2&amp; 3\\ -1&nbsp;&amp; 2\end{bmatrix}$, then $A^{3} + 3A^{2} - 4A + 1$ is equal to<br>

Question 9 :
If $A=\begin{bmatrix}1&amp;1&amp;-1\\2&amp;-3&amp;4\\3&amp;-2&amp;3\end{bmatrix}$ and $B=\begin{bmatrix}-1&amp;-2&amp;-1\\6&amp;12&amp;6\\5&amp;10&amp;5\end{bmatrix}$, then which of the following is/are correct?<br>1. A and B commute.<br>2. AB is null matrix.<br>Select the correct answer using the code given below :

Question 11 :
If $\begin{bmatrix} x &amp; -3 \\ -9 &amp; y \end{bmatrix}\begin{bmatrix} 4 &amp; -3 \\ 9 &amp; 7 \end{bmatrix}=\begin{bmatrix} 1 &amp; 0 \\ 0 &amp; 1 \end{bmatrix},$ then $x=$ .......... $, y $ $=$ ........

Question 12 :
If $A$ be a matrix such that $\displaystyle A \times&nbsp; \begin{bmatrix} 1 &amp; -2 \\ 1 &amp; 4 \end{bmatrix} = \begin{bmatrix} 6 &amp; 0 \\ 0 &amp; 6 \end{bmatrix}$ then $A$ is<br>

Question 13 :
If $A$ and $B$ are two matrices such that $AB$ and $A+B$ are both defined then $A$ and $B$ are&nbsp;

Question 14 :
If $A =&#160;\begin{bmatrix}1 &amp; 2 &amp; 2\\ 2 &amp; 1 &amp; -2\\ a &amp; 2 &amp; b\end{bmatrix}$ is a matrix satisfying $AA^T = 9 I_3$, then the values of $a$ and $b$ are

Question 15 :
If $A=\begin{bmatrix} 4 &amp; -1 \\ -1 &amp; k \end{bmatrix}$ such that $A^{2}-6A+7I=0$, then $k=$

Question 17 :
If matrix $A=[a_{ij}]_{2\times 2}$, where $a_{ij} *1$ if $1*j$ and $0$ if $i=j$ then $A^2$ is equal to

Question 18 :
If $A=\begin{bmatrix} 2 &amp; 5 &amp; -3 \\ -1 &amp; 3 &amp; 1 \\ 4 &amp; 1 &amp; 2 \end{bmatrix}$ then ${A}^{2}$ is

Question 19 :
If $\displaystyle A=\begin{bmatrix} 1 &amp; 0 \\ \cfrac { 1 }{ 2 } &#160;&amp; 1 \end{bmatrix},$ then ${A}^{50}$ is

Question 20 :
If $A+I=\begin{bmatrix} 3 &amp; -2 \\ 4 &amp; 1 \end{bmatrix}$, then $\left( A+I \right) \cdot \left( A-I \right) $ is equal to