# A Short Proof of the Two-sidedness of Matrix Inverses

by Raymond A. Beauregard (University of Rhode Island)

Mathematics Magazine
April, 2007

Subject classification(s): Algebra and Number Theory | Linear Algebra | Matrix Algebra
Applicable Course(s): 3.8 Linear/Matrix Algebra

The paper gives a short proof that for any $$n$$ x $$n$$ matrices $$A$$ and $$C$$ over a field of scalars, $$AC = I$$ if and only if $$CA = I$$. The proof relies on familiarity with elementary matrices and the reduced row echelon form.

A pdf copy of the article can be viewed by clicking below. Since the copy is a faithful reproduction of the actual journal pages, the article may not begin at the top of the first page.