Answered: Let A be a square matrix. ( a ) If A3 =…

Let A be a square matrix. ( a ) If A3 = 0, show that I - A is invertible. ( b ) Suppose A3 - A + I = 0. Show that A is invertible.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...

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Let A be a square matrix.
( a ) If A3 = 0, show that I - A is invertible.

( b ) Suppose A3 - A + I = 0. Show that A is invertible.

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