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A Short Proof of the Two-sidedness of Matrix Inverses

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.

Old Node ID: 
3655
MSC Codes: 
15A04
Author(s): 
Raymond A. Beauregard (University of Rhode Island)
Publication Date: 
Wednesday, April 13, 2011
Original Publication Source: 
Mathematics Magazine
Original Publication Date: 
April, 2007
Subject(s): 
Algebra and Number Theory
Linear Algebra
Matrix Algebra
Topic(s): 
Solving Linear Systems: Elementary Matrices
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Publish Page: 
Furnished by JSTOR: 
Rating Count: 
21.00
Rating Sum: 
63.00
Rating Average: 
3.00
Applicable Course(s): 
3.8 Linear/Matrix Algebra
Modify Date: 
Wednesday, April 13, 2011
Average: 3.1 (22 votes)

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