> [!NOTE] Definiton (Matrix Multiplication) > Let $(R,+,\circ)$ be a [[Rings|ring]]. Let $A,B$ be [[Matrix|matrices over]] $R$ of order $m\times n$ and $n\times l$ respectively. Then product of $A$ and $B,$ denoted $AB,$ is given the $n\times l$ matrix $C$ over $R$ whose $(i,j)$ entry is given by $c_{ij}=\sum_{k=1}^{n} a_{ik}b_{kj}$for all $(i,j)\in[1,2,\dots,m]\times[1,2,\dots,l].$