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## Homework Statement

Let A be a square matrix with right inverse B. To prove A has a left inverse C and that B = C.

## Homework Equations

Matrix multiplication is asociative (AB)C=A(BC).

A has a right inverse B such that AB = I

## 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.