For $A$ an $m\times n$ matrix and $B$ an $n\times p$ matrix with entries $(a_{ij})$ and $(b_{k\ell})$ respectively, the product $C=AB$ is the $m\times p$ matrix whose entries are given by \(c_{ij} = \sum_{k=1}^n a_{ik}b_{kj}\) for $1 \leq i \leq m$ and $1 \leq j \leq m$.
Note that this binary operation is not commutative, and $BA$ may not even be defined even though $AB$ is due to differing dimensions.
Wikidata ID: Q1049914