The multiplication of matrices possesses the following properties, which we state without proof.
1. The associative law For any three matrices A, B and C. We have (AB) C = A (BC), whenever both sides of the equality are defined.
2. The distributive law For three matrices A, B and C.
(i) A (B+C) = AB + AC
(ii) (A+B) C = AC + BC, whenever both sides of equality are defined.
3. The existence of multiplicative identity For every square matrix A, there exist an identity matrix of same order such that IA = AI = A.