Answer
The product of matrix B and matrix A is $\left[ \begin{matrix}
2 & 1 & 3 \\
8 & 1 & 9 \\
5 & 1 & 6 \\
\end{matrix} \right]$.
Work Step by Step
Considered the matrices,
$A=\left[ \begin{matrix}
2 & 1 & 3 \\
1 & -1 & 0 \\
\end{matrix} \right]$ And $B=\left[ \begin{matrix}
1 & 0 \\
3 & 2 \\
2 & 1 \\
\end{matrix} \right]$
Now, use the product rule of matrices,
$\begin{align}
& \text{BA}=\left[ \begin{matrix}
1 & 0 \\
3 & 2 \\
2 & 1 \\
\end{matrix} \right]\left[ \begin{matrix}
2 & 1 & 3 \\
1 & -1 & 0 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
1\cdot 2+0\cdot 1 & 1\cdot 1+0\cdot -1 & 1\cdot 3+0\cdot 0 \\
3\cdot 2+2\cdot 1 & 3\cdot 1+2\cdot -1 & 3\cdot 3+2\cdot 0 \\
2\cdot 2+1\cdot 1 & 2\cdot 1+1\cdot -1 & 2\cdot 3+1\cdot 0 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
2 & 1 & 3 \\
8 & 1 & 9 \\
5 & 1 & 6 \\
\end{matrix} \right]
\end{align}$
Hence, the product of matrix B and matrix A is $\left[ \begin{matrix}
2 & 1 & 3 \\
8 & 1 & 9 \\
5 & 1 & 6 \\
\end{matrix} \right]$.
