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## Homework Statement

Let A be an m x n matrix, and suppose there exist n x m matrices C and D such that CA = In and AD = Im. Prove that C = D.

## Homework Equations

## The Attempt at a Solution

I think it's obvious that C=D=A^(-1). But I'm having trouble proving it since I cannot prove that A is a square matrix and I'm not sure how where to start trying to prove it if A is not square.