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A Short Proof of the Two-sidedness of Matrix Inverses

by Raymond A. Beauregard (University of Rhode Island)

This article originally appeared in:
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.

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Capsule Course Topic(s):
Linear Algebra | Solving Linear Systems: Elementary Matrices
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