Answer
$False$
Work Step by Step
Proof:
Let A and B bet two square matrices.
Let $A = \begin{bmatrix}
1 & 2\\
2 & 3
\end{bmatrix}, B = \begin{bmatrix}
4 & 5\\
6 & 7
\end{bmatrix}$
$\implies AB = \begin{bmatrix}
1 & 2\\
3 & 4
\end{bmatrix}\begin{bmatrix}
5 & 6\\
7 & 8
\end{bmatrix} = \begin{bmatrix}
19 & 22\\
43 & 50
\end{bmatrix}$
$\implies BA = \begin{bmatrix}
5&6\\
7&8
\end{bmatrix}\begin{bmatrix}
1&2\\
3&4
\end{bmatrix} = \begin{bmatrix}
23&34\\
31&46
\end{bmatrix}$
$\implies AB \ne BA$
