Answer
False
Work Step by Step
Let us consider as an example the matrices below:
$A=\left[\begin{array}{ll}
1 & 0\\
1 & 0
\end{array}\right],B=\left[\begin{array}{ll}
0 & 0\\
1 & 1
\end{array}\right]$
Take their multiplication
$AB=\left[\begin{array}{ll}
0 & 0\\
0 & 0
\end{array}\right]$
and
$BA=\left[\begin{array}{ll}
0 & 0\\
2 & 0
\end{array}\right]$
We see that all corresponding entries of AB and BA are not equal, so $AB\neq BA$. This means that the multiplication of matrices is not commutative.
Thus, the statement is false.
