Answer
The matrix multiplication is not commutative.
Work Step by Step
$AB=\begin{bmatrix} -1 & 2 & 0\\ 0&3&2\\0 &1&4 \end{bmatrix} \begin{bmatrix} 2 & -1 & 2 \\ 0 & 2 & 1\\ 3& 0& -1\end{bmatrix}\\=\begin{bmatrix} -2&1+4& -2+2+0 \\ 0+0+6 & 0+6+0 &0+3+2\\0+0+12&0+2+0&0+1+4 \end{bmatrix}$
$ \\ =\begin{bmatrix} -2 & 5 & 0 \\ 6 & 6 & 5 \\ 12 & 2 & 5 \end{bmatrix} $
$BA=\begin{bmatrix} 5 & 1 \\ 0 & -2 \\ 3 & 7 \end{bmatrix} \begin{bmatrix} 4 &-2 \\ 3 & 1 \end{bmatrix} \\=\begin{bmatrix} 20+3 &-10+1 \\ -6& -2\\ 33 &1 \end{bmatrix}\\=\begin{bmatrix} 23 &-9 \\-6 &-2\\ 33 &1 \end{bmatrix}$
So, $AB \ne BA$.
From the previous examples, we can notice that $BC \ne CB$ Aand $AC \ne CA$. This means that the matrix multiplication is not commutative.
