A calculus of the absurd

18.1.5 Properties of matrix multiplication

Matrix multiplication has a number of useful properties, for example

  • • It is associative; we can change the order in which we multiply several matrices together without changing the result (i.e. \((AB)C = A(BC)\)).

  • • Matrix multiplication is distributive over matrix addition (i.e. we can factorise matrices, mathematically: \(A(B + C) = AB + AC\)).

Important: matrix multiplication is not commutative (i.e. \(AB \ne BA\)).