Consider the n ×n matrices A and B and their product AB (a) Show that if AB is invertible, then so is A. (Hint: There is a matrix W such that ABW = I. Why?) (b) Show that if AB is invertible, then so is B.
Consider the n ×n matrices A and B and their product AB (a) Show that if AB is invertible, then so is A. (Hint: There is a matrix W such that ABW = I. Why?) (b) Show that if AB is invertible, then so is B.
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter6: Matrices And Determinants
Section6.2: The Algebra Of Matrices
Problem 61E
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Consider the n ×n matrices A and B and their product AB
(a) Show that if AB is invertible, then so is A.
(Hint: There is a matrix W such that ABW = I. Why?)
(b) Show that if AB is invertible, then so is B.
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