Answer
The statement is false.
Work Step by Step
Consider the following matrices:
$A=\left[ \begin{matrix}
1 & 2 \\
0 & 1 \\
\end{matrix} \right]$
And
$B=\left[ \begin{matrix}
0 & 1 \\
2 & 1 \\
\end{matrix} \right]$
Now calculate AB:
$\begin{align}
& AB=\left[ \begin{matrix}
1 & 2 \\
0 & 1 \\
\end{matrix} \right]\left[ \begin{matrix}
0 & 1 \\
2 & 1 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
0+4 & 1+2 \\
0+2 & 0+1 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
4 & 3 \\
2 & 1 \\
\end{matrix} \right]
\end{align}$
And BA,
$\begin{align}
& BA=\left[ \begin{matrix}
0 & 1 \\
2 & 1 \\
\end{matrix} \right]\left[ \begin{matrix}
1 & 2 \\
0 & 1 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
0+0 & 1+0 \\
2+0 & 4+1 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
0 & 1 \\
2 & 5 \\
\end{matrix} \right]
\end{align}$
Clearly, $AB\ne BA$
Hence, the statement is false.
