The number of matrices of order $3 \times 3$,whose entries are either $0$ or $1$ and the sum of all the entries is a prime number,is:

If $\begin{bmatrix} 2 & 3 & 4 \end{bmatrix} \begin{bmatrix} 1 & x & 3 \\ 2 & 4 & 5 \\ 3 & 2 & x \end{bmatrix} \begin{bmatrix} x \\ 2 \\ 0 \end{bmatrix} = O$,then $x = $ . . . . . .

If $I$ is a unit matrix,then $3I$ will be

Let $A = [a_{ij}]$ be a square matrix of order $3$ such that $a_{ij} = 2^{j-i}$,for all $i, j = 1, 2, 3$. Then,the matrix $A^{2} + A^{3} + \ldots + A^{10}$ is equal to

Evaluate $A^2+2I$ if $A=\begin{bmatrix} 1 & 0 \\ 1 & 2 \end{bmatrix}$. (in $A$)

$\cos \theta \begin{bmatrix} \cos \theta & \sin \theta \\ - \sin \theta & \cos \theta \end{bmatrix} + \sin \theta \begin{bmatrix} \sin \theta & - \cos \theta \\ \cos \theta & \sin \theta \end{bmatrix} = $