Question 1 :
If A = $ \begin{bmatrix} \alpha &amp; 0 \\ 1 &amp; 1\end{bmatrix}$ , B = $ \begin{bmatrix} 1 &amp; 0 \\ 5 &amp; 1\end{bmatrix}$ whenever $A^2 \, = \, B$<br>then values of $\alpha$ is

Question 3 :
$A$ is a $3\times 3$ diagonal matrix having integral entries such that $\text{det}(A)=120$, number of such matrices is $10n$, then $n$ is

Question 4 :
If the order of a matrix is $\displaystyle 20\times 5$ then the number of elements in the matrix is _____

Question 5 :
If A is $3 \times 4$ matrix and B is matrix such that A'B and BA' are both defined, then B is of the type.<br>

Question 6 :
Let $A$ is a square matrix of order $n$ and $a$ being a scalar then $|aA|=$

Question 8 :
If $\left[\begin{array}{ll}<br/>x+3 &amp; 2y+x\\<br/>z-1 &amp; 4a-z<br/>\end{array}\right]=\left[\begin{array}{ll}<br/>0 &amp; -7\\<br/>3 &amp; 2a<br/>\end{array}\right],$ then $(x+y+z+a)$ is:

Question 9 :
If $ \begin{bmatrix} 1/25 &amp; 0 \\ x &amp; 1/25 \end{bmatrix}\quad =\quad \begin{bmatrix} 5 &amp; 0 \\ -a &amp; 5 \end{bmatrix}^{ -2 } $, then the value of x is

Question 10 :
If $\begin{bmatrix} 1 &amp; 1\\ 0 &amp; 1\end{bmatrix} \begin{bmatrix} 1 &amp; 2\\ 0 &amp; 1\end{bmatrix}\begin{bmatrix} 1 &amp; 3\\ 0 &amp; 1\end{bmatrix} ..\begin{bmatrix} 1 &amp; n-1\\ 0 &amp; 1\end{bmatrix} =\begin{bmatrix} 1 &amp; 78\\ 0 &amp; 1\end{bmatrix}$, then the inverse of $\begin{bmatrix} 1 &amp; n\\ 0 &amp; 1\end{bmatrix}$ is?

Question 11 :
Consider $A$ and $B$ two square matrices of same order. Select the correct alternative.

Question 12 :
If the number of elements in a matrix is $60$ then how many different order of matrix are possible

Question 13 :
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>

Question 14 :
Out of the following matrices, choose that matrix which is a scalar matrix.

Question 15 :
If D$_1$ and D$_2$ are two 3 $\times$ 3 diagonal matrices, then which of the following is/are true?

Question 16 :
<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 17 :
Assertion: If $D = diag [d_1, d_2, ...., d_n]$, then $D^{-1} = diag [d_1^{-1}, d_2^{-1} ..... , d_n^{-1}]$ Reason: If $D = diag [d_1, d_2, ...... d_n], $ then $D^n = diag [d_1^n, d_2^n ...... , d_n^n].$

Question 18 :
Two rectangular matrices of order $n\times m$ and $m\times k$ are multiplied in the same order. The resulting matrix formed is a:

Question 19 :
If $A$ is $2\times 3$ matrix and $AB$ is a $2\times 5$ matrix, then $B$ must be a

Question 20 :
What is the inverse of the matrix<br/>$A=\begin{bmatrix} \cos { \theta } &amp; \sin { \theta } &amp; 0 \\ -\sin { \theta } &amp; \cos { \theta } &amp; 0 \\ 0 &amp; 0 &amp; 1 \end{bmatrix}$ ?