# Matrix multiplication

1. Sep 29, 2011

### P-Jay1

A is an M × N matrix, B is N × K and C is a K × L matrix. Consider matrix
multiplication (AB)ij = Pk AikBkj .

Using the formula, (AB)ij = Pk AikBkj, how would I calculate ((AB)C) and (A(BC))?

2. Sep 29, 2011

### Fredrik

Staff Emeritus
Just use the formula twice (on each of those products). Start with $$((AB)C)_{ij}=\sum_k(AB)_{ik}C_{kj}.$$ Now use the formula again to evaluate $(AB)_{ik}$.