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

If $A$ and $B$ are square matrices of order $3 \times 3$,$A$ is non-singular,and $AB = O$,then $B$ is a:

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 $A = \begin{bmatrix} 1 & -2 & 1 \\ 2 & 1 & 3 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & 1 \\ 3 & 2 \\ 1 & 1 \end{bmatrix}$,then $(AB)^T$ is equal to

Which of the given values of $x$ and $y$ make the following pair of matrices equal?
$\left[\begin{array}{cc}3x+7 & 5 \\ y+1 & 2-3x\end{array}\right]=\left[\begin{array}{cc}0 & y-2 \\ 8 & 4\end{array}\right]$

If $A = \begin{bmatrix} 1 & 0 \\ 2 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & 0 \\ 1 & 12 \end{bmatrix}$,then: