Given $\;$ $\begin{bmatrix}
2 & -1 \\
0 & 3
\end{bmatrix} \begin{bmatrix}
0 & 2 \\
1 & -4
\end{bmatrix} = A + 7 I$
Find matrix $A$ if $I$ is an unit matrix of order $2 \times 2$.
$I$ is an unit matrix of order $2 \times 2$
$\therefore \;$ $I = \begin{bmatrix}
1 & 0 \\
0 & 1
\end{bmatrix}$
Now, $\;$ $\begin{bmatrix}
2 & -1 \\
0 & 3
\end{bmatrix} \begin{bmatrix}
0 & 2 \\
1 & -4
\end{bmatrix} = A + 7 I$
$\implies$ $\begin{bmatrix}
2 \times 0 + \left(-1\right) \times 1 & 2 \times 2 + \left(-1\right) \times \left(-4\right) \\
0 \times 0 + 3 \times 1 & 0 \times 2 + 3 \times \left(-4\right)
\end{bmatrix} = A + 7 \times \begin{bmatrix}
1 & 0 \\
0 & 1
\end{bmatrix}$
i.e. $\;$ $\begin{bmatrix}
-1 & 8 \\
3 & -12
\end{bmatrix} = A + \begin{bmatrix}
7 & 0 \\
0 & 7
\end{bmatrix}$
i.e. $\;$ $\begin{bmatrix}
-1 & 8 \\
3 & -12
\end{bmatrix} - \begin{bmatrix}
7 & 0 \\
0 & 7
\end{bmatrix} = A$
i.e. $\;$ $A = \begin{bmatrix}
-1 - 7 & 8 - 0 \\
3 - 0 & -12 - 7
\end{bmatrix}$
i.e. $\;$ $A = \begin{bmatrix}
-8 & 8 \\
3 & -19
\end{bmatrix}$