Answer
The matrix $ BA $ is, $ BA=\left[ \begin{matrix}
-10 & -6 & 2 \\
16 & 3 & 4 \\
-23 & -16 & 7 \\
\end{matrix} \right]$
Work Step by Step
Here we need to find $ BA $. Therefore consider, $\begin{align}
& BA=\left[ \begin{array}{*{35}{l}}
0 & -2 \\
3 & 2 \\
1 & -5 \\
\end{array} \right]\left[ \begin{array}{*{35}{l}}
2 & -1 & 2 \\
5 & 3 & -1 \\
\end{array} \right] \\
& =\left[ \begin{matrix}
0\left( 2 \right)-2\left( 5 \right) & 0\left( -1 \right)-2\left( 3 \right) & 0\left( 2 \right)-2\left( -1 \right) \\
3\left( 2 \right)+2\left( 5 \right) & 3\left( -1 \right)+2\left( 3 \right) & 3\left( 2 \right)+2\left( -1 \right) \\
1\left( 2 \right)-5\left( 5 \right) & 1\left( -1 \right)-5\left( 3 \right) & 1\left( 2 \right)-5\left( -1 \right) \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
-10 & -6 & 2 \\
6+10 & -3+6 & 6-2 \\
2-25 & -1-15 & 2+5 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
-10 & -6 & 2 \\
16 & 3 & 4 \\
-23 & -16 & 7 \\
\end{matrix} \right]
\end{align}$
Thus, $ BA=\left[ \begin{matrix}
-10 & -6 & 2 \\
16 & 3 & 4 \\
-23 & -16 & 7 \\
\end{matrix} \right]$
