# What are some sample matrix multiplication problems?

The product of two square matrices (a square matrix is a matrix that has the same number of rows and columns) $A B$ is not always equal to $B A$. Try it with $A = \left(\begin{matrix}0 & 1 \\ 0 & 0\end{matrix}\right)$ and $B = \left(\begin{matrix}0 & 0 \\ 0 & 1\end{matrix}\right)$.
In order to calculate the product of two rectangular matrices $C$ and $D$, if you want $C D$ you need $C$ to have the same number of columns as the number of rows of $D$. If you want $D C$ it's the same problem with the number of columns of $D$ and the number of lines of $C$.