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Question: Let A and B be nxn matrices such that AB is invertible. Prove that A and B are invertible.

All I have so far is that there exists a matrix C such that

(AB)C = I and C(AB) = I.

How do I use this to show that there exists D such that AD = DA = I and that there exists E such that BE = EB = I ???

All I have so far is that there exists a matrix C such that

(AB)C = I and C(AB) = I.

How do I use this to show that there exists D such that AD = DA = I and that there exists E such that BE = EB = I ???

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