Definition MM Matrix Multiplication

Suppose $A$ is an $m\times n$ matrix and $\vectorlist{B}{p}$ are the columns of an $n\times p$ matrix $B$. Then the matrix product of $A$ with $B$ is the $m\times p$ matrix where column $i$ is the matrix-vector product $A\vect{B}_i$. Symbolically, \begin{equation*} AB=A\matrixcolumns{B}{p}=\left[A\vect{B}_1|A\vect{B}_2|A\vect{B}_3|\ldots|A\vect{B}_p\right]. \end{equation*}