If A ∈ R^n×n is invertible, then columns of A^−1 are linearly independent. Explain why.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter7: Systems Of Equations And Inequalities
Section7.7: Solving Systems With Inverses
Problem 4SE: Can a matrix with an entire column of zeros have an inverse? Explain why or why not.
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 If A ∈ R^n×n is invertible, then columns of A^−1 are linearly independent. Explain why. 

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