If $\mathrm{A}=\left[\begin{array}{rr}0& 2\\ 5& -2\end{array}\right],\mathrm{B}=\left[\begin{array}{rr}1& -1\\ 3& 2\end{array}\right]$ and $\mathrm{I}$ is a  unit matrix of order $2\times 2,$ find :

${\mathrm{A}}^2$

If $\mathrm{A}=\left[\begin{array}{rr}0& 2\\ 5& -2\end{array}\right],\mathrm{B}=\left[\begin{array}{rr}1& -1\\ 3& 2\end{array}\right]$ and $\mathrm{I}$ is a unit matrix of order$2\times 2,$ find :

${\mathrm{B}}^2\mathrm{A}$

Find $\mathrm{x}$ and $\mathrm{y}$ if :

$\left[\begin{array}{cc}4& 3\mathrm{x}\\ \mathrm{x}& -2\end{array}\right]\left[\begin{array}{l}5\\ 1\end{array}\right]=\left[\begin{array}{l}\mathrm{y}\\ 8\end{array}\right]$

Find $\mathrm{x}$ and $\mathrm{y}$ if :

$\left[\begin{array}{rr}\mathrm{x}& 0\\ -3& 1\end{array}\right]\left[\begin{array}{rr}1& 1\\ 0& \mathrm{y}\end{array}\right]=\left[\begin{array}{rr}2& 2\\ -3& -2\end{array}\right]$

If$\mathrm{A}=\left[\begin{array}{ll}1& 3\\ 2& 4\end{array}\right],\mathrm{B}=\left[\begin{array}{ll}1& 2\\ 4& 3\end{array}\right]$ and $\mathrm{C}=\left[\begin{array}{ll}4& 3\\ 1& 2\end{array}\right],$ find :

$\left(\mathrm{i}\right) \left(\mathrm{AB}\right) \mathrm{C}$

$\left(\mathrm{ii}\right) \mathrm{A} \left(\mathrm{BQ}\right)$

$\mathrm{Is} \mathrm{A} \left(\mathrm{BQ}\right) = \left(\mathrm{AB}\right) \mathrm{C} ?$

Given $\mathrm{A}=\left[\begin{array}{ccc}0& 4& 6\\ 3& 0& -1\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{rr}0& 1\\ -1& 2\\ -5& -6\end{array}\right],$ is the following possible :

$AB$

Given $\mathrm{A}=\left[\begin{array}{ccc}0& 4& 6\\ 3& 0& -1\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{rr}0& 1\\ -1& 2\\ -5& -6\end{array}\right],$ is the following possible :

$\mathrm{BA}$

Given $\mathrm{A}=\left[\begin{array}{ccc}0& 4& 6\\ 3& 0& -1\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{rr}0& 1\\ -1& 2\\ -5& -6\end{array}\right],$ is the following possible :

${\mathrm{A}}^2.$