If $A$ and $B$ are square matrices of the same order,then which of the following properties holds true?

In the matrix $A = \begin{bmatrix} 2 & 5 & 19 & -7 \\ 35 & -2 & \frac{5}{2} & 12 \\ \sqrt{3} & 1 & -5 & 17 \end{bmatrix}$,write:
$(i)$ The order of the matrix
$(ii)$ The number of elements
$(iii)$ The elements $a_{13}, a_{21}, a_{33}, a_{24}, a_{23}$

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

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$,then $A^{2} - 5A$ is equal to:

If $A = \begin{bmatrix} 0 & -\tan(\frac{\theta}{2}) \\ \tan(\frac{\theta}{2}) & 0 \end{bmatrix}$ and $(I_{2} + A)(I_{2} - A)^{-1} = \begin{bmatrix} a & -b \\ b & a \end{bmatrix}$,then $13(a^{2} + b^{2})$ is equal to ...........

For the matrices $A$ and $B$,verify that $(AB)^{\prime} = B^{\prime}A^{\prime}$ where $A = \begin{bmatrix} 1 \\ -4 \\ 3 \end{bmatrix}$ and $B = \begin{bmatrix} -1 & 2 & 1 \end{bmatrix}$.