Mathematics — Linear Algebra · matrix-multiplication
Problem
Prove that matrix multiplication is associative. In other words, suppose A, B, and C are matrices whose sizes are such that (AB)C makes sense. Explain why A(BC) makes sense and prove that
(AB)C=A(BC).
Try to find a clean proof that illustrates the following quote from Emil Artin: ``It is my experience that proofs involving matrices can be shortened by 50\% if one throws the matrices out.''