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matrix multiplication

Multiplying two matrices, $A$ then $B$ ; entry $(i,j)$ of $AB$ is row $i$ of $A$ dotted with column $j$ of $B$ . Defined only when $A$ 's column count equals $B$ 's row count.

Examples

$\begin{pmatrix}1&2\\3&4\end{pmatrix}\begin{pmatrix}5&6\\7&8\end{pmatrix} = \begin{pmatrix}19&22\\43&50\end{pmatrix}$ .