In number arithmetic every number a ( 0 ) has a reciprocal b written as a 1 or 1 a such that b a = a b = 1 . Some, but not all, square matrices have inverses. If a square matrix A has an inverse, A 1 , then

A A 1 = A 1 A = I .

We develop a rule for finding the inverse of a 2 × 2 matrix (where it exists) and we look at two methods of finding the inverse of a 3 × 3 matrix (where it exists).

Non-square matrices do not possess inverses so this Section only refers to square matrices.


Learning Outcomes