Find the values of $x$ and $y$ from the following equation:
$2\begin{bmatrix} x & 5 \\ 7 & y-3 \end{bmatrix} + \begin{bmatrix} 3 & -4 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 7 & 6 \\ 15 & 14 \end{bmatrix}$

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 $A$ and $B$ are square matrices of order $n \times n$,then ${(A - B)^2}$ is equal to

Consider the following information regarding the number of men and women workers in three factories $I, II$ and $III$.

Factory	Men and Women Workers
$I$	$30$ Men,$25$ Women
$II$	$25$ Men,$31$ Women
$III$	$27$ Men,$26$ Women

Represent the above information in the form of a $3 \times 2$ matrix. What does the entry in the third row and second column represent?

If $M = \begin{bmatrix} \frac{5}{2} & \frac{3}{2} \\ -\frac{3}{2} & -\frac{1}{2} \end{bmatrix}$,then which of the following matrices is equal to $M^{2022}$?

If $A = \begin{bmatrix} 1 & -2 & 3 \\ -4 & 2 & 5 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & 3 \\ 4 & 5 \\ 2 & 1 \end{bmatrix}$,then find $AB$ and $BA$. Show that $AB \neq BA$.