1. The problem statement, all variables and given/known data Let A be a square matrix with right inverse B. To prove A has a left inverse C and that B = C. 2. Relevant equations Matrix multiplication is asociative (AB)C=A(BC). A has a right inverse B such that AB = I 3. The attempt at a solution I dont really know where to start, I mean, proving that if both B and C exist then B = C is not that hard, but I really cant get around proving one implies the other.