Answer
a) $AB=\left[ \begin{matrix}
-1 & -2 & -3 \\
-2 & -4 & -6 \\
-3 & -6 & -9 \\
\end{matrix} \right]$
b) $BA=\left[ -14 \right]$
Work Step by Step
(a)
Consider the product,
$\begin{align}
& AB=\left[ \begin{matrix}
-1 \\
-2 \\
-3 \\
\end{matrix} \right]\left[ \begin{matrix}
1 & 2 & 3 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
-1\left( 1 \right) & -1\left( 2 \right) & -1\left( 3 \right) \\
-2\left( 1 \right) & -2\left( 2 \right) & -2\left( 3 \right) \\
-3\left( 1 \right) & -3\left( 2 \right) & -3\left( 3 \right) \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
-1 & -2 & -3 \\
-2 & -4 & -6 \\
-3 & -6 & -9 \\
\end{matrix} \right]
\end{align}$
So that,
$AB=\left[ \begin{matrix}
-1 & -2 & -3 \\
-2 & -4 & -6 \\
-3 & -6 & -9 \\
\end{matrix} \right]$
(b)
Consider the product,
$\begin{align}
& BA=\left[ \begin{matrix}
1 & 2 & 3 \\
\end{matrix} \right]\left[ \begin{matrix}
-1 \\
-2 \\
-3 \\
\end{matrix} \right] \\
& =\left[ 1\left( -1 \right)+2\left( -2 \right)+3\left( -3 \right) \right] \\
& =\left[ -1-4-9 \right] \\
& =\left[ -14 \right]
\end{align}$
