# A calculus of the absurd

##### 22.1.5 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. $$AB \ne BA$$).