OK here is the problem

Suppose $\displaystyle \mathbf{A}\text{ is an }m\times n\text{ matrix and there exist matrices }\mathbf{C}\text{ and }\mathbf{D}\text{ such that }\mathbf{CA}=\mathbf{I}_n\text{ and }\\\mathbf{AD}=\mathbf{I}_m\text{. Prove that }m=n$

im soo clueless =( any help would be awesome