Answer
True.
Work Step by Step
Suppose that $A$ and $B$ represent two $m$ by $n$ matrices.
The sum, $A+B,$ is defined as the $m$ by $n$ matrix formed by adding the corresponding entries $a_{ij}$ of $A$ and $b_{ij}$ of $B$.
Since addition of real numbers is commutative, it follows that
$a_{ij}+b_{ij}=b_{ij}+a_{ij}$
and
$A+B=B+A.$
The statement is true.
