# 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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File Content:
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