Answer
The matrix $ BD $ is, $ BD=\left[ \begin{matrix}
-6 & 4 & -8 \\
0 & 5 & 11 \\
-17 & 13 & -19 \\
\end{matrix} \right]$.
Work Step by Step
Here we need to find $ BD $. Therefore consider, $\begin{align}
& BD=\left[ \begin{array}{*{35}{l}}
0 & -2 \\
3 & 2 \\
1 & -5 \\
\end{array} \right]\left[ \begin{array}{*{35}{l}}
-2 & 3 & 1 \\
3 & -2 & 4 \\
\end{array} \right] \\
& =\left[ \begin{matrix}
0\left( -2 \right)-2\left( 3 \right) & 0\left( 3 \right)-2\left( -2 \right) & 0\left( 1 \right)-2\left( 4 \right) \\
3\left( -2 \right)+2\left( 3 \right) & 3\left( 3 \right)+2\left( -2 \right) & 3\left( 1 \right)+2\left( 4 \right) \\
1\left( -2 \right)-5\left( 3 \right) & 1\left( 3 \right)-5\left( -2 \right) & 1\left( 1 \right)-5\left( 4 \right) \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
-6 & 4 & -8 \\
-6+6 & 9-4 & 3+8 \\
-2-15 & 3+10 & 1-20 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
-6 & 4 & -8 \\
0 & 5 & 11 \\
-17 & 13 & -19 \\
\end{matrix} \right]
\end{align}$
Thus, $ BD=\left[ \begin{matrix}
-6 & 4 & -8 \\
0 & 5 & 11 \\
-17 & 13 & -19 \\
\end{matrix} \right]$
