Question 1 :
The number of all possible matrices of order $3 \times 3$ with each entry $0$ or $1$ is:

Question 2 :
A matrix having $m$ rows and $n$ columns with $m \displaystyle \neq n$ is said to be a

Question 5 :
If the matrix $\begin{bmatrix} 1 & 3 & \lambda +2 \\ 2 & 4 & 8 \\ 3 & 5 & 10 \end{bmatrix}$ is singular, then $\lambda=$

Question 7 :
$\displaystyle \begin{bmatrix}1 &amp;0 &amp;0 \\0 &amp;4 &amp;0 \\0 &amp;0 &amp;5 \end{bmatrix}$<span> is an:</span>

Question 8 :
If $\begin{bmatrix}4 &amp;-3 \\ 2 &amp; 16\end{bmatrix}$ = $\begin{bmatrix}4 &amp;-3 \\ 2 &amp; 2^t\end{bmatrix}$, then t = _______

Question 10 :
Matrix $A$ is given by $A=\begin{bmatrix} 6 &amp; 11 \\ 2 &amp; 4 \end{bmatrix}$ then the determinant of ${A}^{2015} -6{A}^{2014} $ is.

Question 11 :
Matrix $A = [a_{ij}]_{m \times n}$ is a square matrix if<br>

Question 12 :
If the order of a matrix is $\displaystyle 20\times 5$ then the number of elements in the matrix is _____

Question 13 :
If $A=\begin{bmatrix} 2 &amp;-3 \\ -4&amp;-1 \end{bmatrix}$, then adj $(3A^{2}+12A)$ is equal to:

Question 14 :
<b>If $A={ \left[ { a }_{ ij } \right] }_{ 2\times 2 }$ where ${ a }_{ 15 }=\begin{cases} i+j \\ { i }^{ 2 }-2j \end{cases}\begin{matrix} i\neq j \\ i=j \end{matrix}$ then ${ A }^{ -1 }=$</b>

Question 15 :
Let $A$ is a square matrix of order $n$ and $a$ being a scalar then $|aA|=$

Question 16 :
If $A$ and $B$ are matrices of order $3\times 2$ and $C$ is of order $2\times 3$, then which of the following matrices is not defined-

Question 17 :
<div>Find the value of </div><div><br/></div>$A=\begin{vmatrix} 1 &amp; 5 &amp; 7 \\ 5 &amp; 25 &amp; 35 \\ 12 &amp; 20 &amp; 24 \end{vmatrix}$<br/>

Question 18 :
Obtain the inverse of the following matrix using elementary operation:<br/>$A = \begin{bmatrix} 3 &amp; 0 &amp; -1 \\ 2 &amp; 3 &amp; 0 \\ 0 &amp; 4 &amp; 1 \end{bmatrix}$<br/>

Question 20 :
Let $A=\begin{bmatrix} 1 &amp; -1 &amp; -1 \\ 2 &amp; 1 &amp; -3 \\ 1 &amp; 1 &amp; 1 \end{bmatrix}$ and $10B=\begin{bmatrix} 4 &amp; 2 &amp; 2 \\ -5 &amp; 0 &amp; \alpha \\ 1 &amp; -2 &amp; 3 \end{bmatrix}$, if $B$ is the inverse of matrix $A$, then $\alpha $ is

Question 21 :
<div>If $0\le\left[x\right]&lt;2,\,-1\le\left[y\right]&lt;1$ and $1\le\left[z\right]&lt;3$ ( $\left[.\right]$ denotes the greatest integer function) then the maximum value of determinant</div><div>$\Delta=\left| \begin{matrix} \left[x\right]+1 &amp; \left[y\right] &amp; \left[z\right] \\ \left[x\right] &amp; \left[y\right]+1 &amp; \left[z\right] \\ \left[x\right] &amp; \left[y\right] &amp; \left[z\right]+1 \end{matrix} \right|$ is</div>

Question 22 :
If D$_1$ and D$_2$ are two 3 $\times$ 3 diagonal matrices, then which of the following is/are true?

Question 23 :
Consider $A$ and $B$ two square matrices of same order. Select the correct alternative.

Question 24 :
$\left[ \begin{matrix} x \\ 3 \end{matrix}\begin{matrix} 6 \\ 2x \end{matrix} \right]$ is a singular matrix, then $x$ is equal to

Question 25 :
Let $n\ge 2$ be an integer,<div><br/>$A=\begin{bmatrix} \cos { \left( { \dfrac{2\pi}n} \right) } &amp; \sin { \left(\dfrac{2\pi}n \right) } &amp; 0 \\ -\sin { \left( \dfrac{2\pi}n \right) } &amp; \cos { \left(\dfrac{2\pi}n \right) } &amp; 0 \\ 0 &amp; 0 &amp; 1 \end{bmatrix}$ and $I$ is the identity matrix of order $3$., then following of which is correct</div>