Question: Let A and B be nxn matrices such that AB is invertible. Prove that A and B are invertible.(adsbygoogle = window.adsbygoogle || []).push({});

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 ???

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Inverse of a matrix

**Physics Forums | Science Articles, Homework Help, Discussion**