Why in these matrices are $AB=BA$ not equal? What is the logic behind them? We know that in matrices AB=BA.Why in this Matrices $A=\begin{bmatrix} -1 & 3\\
 2 & 0\end{bmatrix}$, $B=\begin{bmatrix} 1 & 2\\
-3 & -5\end{bmatrix}$ are not equal to $AB=BA$. WHY? This is matrix  of order $2\times 2$ for both $A$ and $B$.

Matrix multiplication is generally not commutative unless they're both equal or they're inverses (in which case you will obtain the identity).
