Associativity of matrix multiplication
= Associativity of matrix multiplication
For dimension-compatible <matrices>, $(AB)C=A(BC)$. In coordinates both sides have $(i,j)$ entry $\sum_{k,l}A_{ik}B_{kl}C_{lj}$; distributing and regrouping the finite <sums> proves equality. This permits accumulating a product left to right even when a recursive <algorithm> groups the same transformations from the right. It does not permit changing factor order, because <matrix multiplication> is generally not <commutative>.