5. Prove that if a matrix A is invertible and diagonalizable, then matrix A-1 is also diago- nalizable.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.6: Matrices
Problem 21E: Suppose that A is an invertible matrix over and O is a zero matrix. Prove that if AX=O, then X=O.
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5. Prove that if a matrix A is invertible and diagonalizable, then matrix A-1 is also diago-
nalizable.
Transcribed Image Text:5. Prove that if a matrix A is invertible and diagonalizable, then matrix A-1 is also diago- nalizable.
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