| context | $R$ … ring |
| context | $m,n,k\in \mathbb N$ |
| definiendum | $ *: \mathrm{Matrix}(m,n,R)\times \mathrm{Matrix}(n,k,R)\to \mathrm{Matrix}(m,k,R) $ |
| postulate | $ (A*B)_{ij}=\sum_{l=1}^m A_{il}\cdot B_{lj} $ |
For square matrices, the matrix product is associative. And also for general matrices, we still have $(A*B)*'C=A*''(B*'''C)$, where the four binary functions are the matrix products for the suitable dimensions.