Answer
$\left[\begin{array}{lll}
-6 & 4 & -8\\
0 & 5 & 11\\
-17 & 13 & -19
\end{array}\right]$
Work Step by Step
The product of an $m\times n$ matrix and an $n\times p$ matrix is an $m\times p$ matrix.
The element in the ith row and $j$th column of $BD$ is found by
multiplying each element in the $i$th row of $B$ by the corresponding element in the $j$th column of $D$
and adding the products.
$B$ is a $3\times\underline{2}$ matrix, $D$ is $\underline{2}\times 3.$
$BD$ exists and is a $3\times 3$ matrix.
$BD=\left[\begin{array}{lll}
0(-2)-2(3) & 0(3)-2(-2) & 0(1)-2(4)\\
3(-2)+2(3) & 3(3)+2(-2) & 3(1)+2(41)\\
1(-2)-5(3) & 1(3)-5(-2) & 1(1)-5(4)
\end{array}\right]$
$=\left[\begin{array}{lll}
-6 & 4 & -8\\
0 & 5 & 11\\
-17 & 13 & -19
\end{array}\right]$
