Two-sidedness of Matrix Inverse: A Proof from Scratch
YAP Von Bing
National University of Singapore,
Singapore
Published in The Mathematician Educator, 2024, Vol 5, No. 2, pp 91-95.
Abstract
If n x n matrices A and V satisfy AV=I, then VA=I. This fact is proved using the concepts of linear independence and spanning defined only for n vectors in Rn . The concepts and associated facts then generalise smoothly to any number of vectors, affording a scaffolded approach for learning linear algebra.
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