The discussion focuses on calculating matrix multiplication for the expressions ((AB)C) and (A(BC)) using the formula (AB)ij = Σk AikBkj. It establishes that to compute ((AB)C)_{ij}, one must first calculate (AB)_{ik} and then apply the multiplication with matrix C. The process involves applying the matrix multiplication formula twice, ensuring accurate results for both expressions. This method is crucial for understanding the associative property of matrix multiplication.
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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}.P-Jay1 said: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))?