Order of operations for multiplying three matrices
math.stackexchange.com › questions › 2601451Matrix multiplication is associative, i.e. ( A B) C = A ( B C) for every three matrices where multiplication makes sense (i.e. the sizes are right). For the record, the proof goes something like this: if A = ( A i j) 1 ≤ i ≤ m, 1 ≤ j ≤ n ( m × n matrix), B = ( B j k) 1 ≤ j ≤ n, 1 ≤ k ≤ p ( n × p matrix) and C = ( C k l) 1 ≤ k ≤ p, 1 ≤ l ≤ q ( p × q matrix), then both ( A B) C and A ( B C) will be m × q matrices.