Answer
$\left[\begin{array}{lll}
-10 & -6 & 2\\
16 & 3 & 4\\
-23 & -16 & 7
\end{array}\right]$
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 $BA$ is found by
multiplying each element in the $i$th row of $B$ by the corresponding element in the $j$th column of $A$
and adding the products.
$B$ is a $3\times\underline{2}$ matrix, $A$ is $\underline{2}\times 3.$
$BA $ exists and is a $3\times 3$ matrix.
$BA=\left[\begin{array}{lll}
0(2)-2(5) & 0(-1)-2(3) & 0(2)-2(-1)\\
3(2)+2(5) & 3(-1)+2(3) & 3(2)+2(-1)\\
1(2)-5(5) & 1(-1)-5(3) & 1(2)-5(-1)
\end{array}\right]$
$=\left[\begin{array}{lll}
-10 & -6 & 2\\
16 & 3 & 4\\
-23 & -16 & 7
\end{array}\right]$
