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

The paper gives a proof that for any $$n$$ x $$n$$ matrices $$A$$ and $$C$$ over a field of scalars, $$AC = I$$ if and only if $$CA = I$$.

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