If $A = \begin{bmatrix} i & 1 \\ 0 & i \end{bmatrix}$,then $A^4$ equals

If $A = \begin{bmatrix} 2 & 2 \\ a & b \end{bmatrix}$ and $A^2 = O$,then $(a, b) = $

Two farmers,Ramkishan and Gurcharan Singh,cultivate only three varieties of rice: Basmati,Permal,and Naura. The sales (in Rupees) of these varieties of rice by both farmers in the months of September and October are given by the following matrices $A$ and $B$.
September Sales (in Rupees)
$A = \begin{bmatrix} \text{Basmati} & \text{Permal} & \text{Naura} \\ 10,000 & 20,000 & 30,000 \\ 50,000 & 30,000 & 10,000 \end{bmatrix} \begin{matrix} \\ \text{Ramkishan} \\ \text{Gurcharan Singh} \end{matrix}$
October Sales (in Rupees)
$B = \begin{bmatrix} \text{Basmati} & \text{Permal} & \text{Naura} \\ 5,000 & 10,000 & 6,000 \\ 20,000 & 10,000 & 10,000 \end{bmatrix} \begin{matrix} \\ \text{Ramkishan} \\ \text{Gurcharan Singh} \end{matrix}$
$(i)$ Find the combined sales in September and October for each farmer in each variety.
$(ii)$ Find the decrease in sales from September to October.
$(iii)$ If both farmers receive $2\%$ profit on gross sales,compute the profit for each farmer and for each variety sold in October.

If $A = \begin{bmatrix} 0 & 2 \\ 3 & -4 \end{bmatrix}$ and $kA = \begin{bmatrix} 0 & 3a \\ 2b & 24 \end{bmatrix}$,then the values of $k, a, b$ are respectively

If $ A=\left[\begin{array}{cc}0 & 1 \\ 1 & 0\end{array}\right] $,then $ A^{2} $ is equal to:

If $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} \frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2} \end{bmatrix}$,then $(BB^TA)^5$ is equal to