Matrix Multiplication: Calculating (AB)C and A(BC) Using the Formula

[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))?

 

[Fredrik]

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))?

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}.