Answer
$3B-2A=\begin{bmatrix}
-3 & 11
\\
-10 & 6
\end{bmatrix}$
Work Step by Step
Multiplying each element of $
B=
\begin{bmatrix}
1 & 3
\\
-2 & 2
\end{bmatrix}
$ by $3,$ then
\begin{align*}
3B&=
\begin{bmatrix}
1(3) & 3(3)
\\
-2(3) & 2(3)
\end{bmatrix}
\\\\&=
\begin{bmatrix}
3 & 9
\\
-6 & 6
\end{bmatrix}
.\end{align*}
Multiplying each element of $
A=
\begin{bmatrix}
3 & -1
\\
2 & 0
\end{bmatrix}
$ by $2,$ then
\begin{align*}
2A&=
\begin{bmatrix}
3(2) & -1(2)
\\
2(2) & 0(2)
\end{bmatrix}
\\\\&=
\begin{bmatrix}
6 & -2
\\
4 & 0
\end{bmatrix}
.\end{align*}
Combining the results above gives
\begin{align*}
3B-2A&=
\begin{bmatrix}
3 & 9
\\
-6 & 6
\end{bmatrix}
-
\begin{bmatrix}
6 & -2
\\
4 & 0
\end{bmatrix}
\\\\&=
\begin{bmatrix}
3-6 & 9-(-2)
\\
-6-4 & 6-0
\end{bmatrix}
\\\\&=
\begin{bmatrix}
3-6 & 9+2
\\
-6-4 & 6-0
\end{bmatrix}
\\\\&=
\begin{bmatrix}
-3 & 11
\\
-10 & 6
\end{bmatrix}
.\end{align*}
Hence, $
3B-2A=\begin{bmatrix}
-3 & 11
\\
-10 & 6
\end{bmatrix}
.$
