For $3 \times 3$ order matrices $A$ and $B$,which of the following is generally true?

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 $AB \neq BA$.

Construct a $2 \times 2$ matrix,$A = [a_{ij}]$,whose elements are given by: $a_{ij} = \frac{(i + 2j)^2}{2}$

If matrix $A = \begin{bmatrix} 1 & 3k + \frac{1}{3} \\ 0 & 1 \end{bmatrix}$,then the value of $\prod_{k=1}^{36} \begin{bmatrix} 1 & 3k + \frac{1}{3} \\ 0 & 1 \end{bmatrix}$ is equal to :-

If $I$ is a unit matrix of order $10$,then the determinant of $I$ is equal to

The matrix $A = \frac{1}{3}\begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ -2 & 2 & -1 \end{bmatrix}$ is