If $A=\left[\begin{array}{ccc}2 & -3 & 5 \\ -1 & 0 & 3\end{array}\right]$ and $B=\left[\begin{array}{ccc}3 & 2 & -2 \\ 4 & -3 & 1\end{array}\right]$, verify that $(A+B)=(B+A)$
$A+B=\left[\begin{array}{ccc}2 & -3 & 5 \\ -1 & 0 & 3\end{array}\right]+\left[\begin{array}{ccc}3 & 2 & -2 \\ 4 & -3 & 1\end{array}\right]$
$=\left[\begin{array}{lll}5 & -1 & 3 \\ 3 & -3 & 4\end{array}\right]$
$B+A=\left[\begin{array}{ccc}3 & 2 & -2 \\ 4 & -3 & 1\end{array}\right]+\left[\begin{array}{ccc}2 & -3 & 5 \\ -1 & 0 & 3\end{array}\right]$
$=\left[\begin{array}{lll}5 & -1 & 3 \\ 3 & -3 & 4\end{array}\right]=\mathrm{B}+\mathrm{A}$
Therefore, $A+B=B+A$
This is true for any matrix
Conclusion: $A+B=B+A$
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