Answer
$A=\begin{bmatrix}4&3\\4&1\end{bmatrix},B=\begin{bmatrix}1&2\\3&0\end{bmatrix}$
Work Step by Step
In order to find two matrices $A$, $B$ so that the given equation is checked, we will take an arbitrary matrix $B$ and determine the matrix $A$. (We could also take a random matrix $A$ and calculate $B$.) The two matrices must be $2\times 2$.
$$B=\begin{bmatrix}1&2\\3&0\end{bmatrix}$$
We have:
$$\begin{align*}
2A-3\begin{bmatrix}1&2\\3&0\end{bmatrix}&=\begin{bmatrix}5&0\\-1&2\end{bmatrix}\\
2A-\begin{bmatrix}3&6\\9&0\end{bmatrix}&=\begin{bmatrix}5&0\\-1&2\end{bmatrix}\\
2A&=\begin{bmatrix}5&0\\-1&2\end{bmatrix}+\begin{bmatrix}3&6\\9&0\end{bmatrix}\\
2A&=\begin{bmatrix}8&6\\8&2\end{bmatrix}\\
A&=\begin{bmatrix}4&3\\4&1\end{bmatrix}.
\end{align*}$$
