Find an example of a 2 x 2 matrix A such that A? + I2, A3 + I2, and A6 = I2. Explain how you know, without calculating, that A4 must be invertible.
Find an example of a 2 x 2 matrix A such that A? + I2, A3 + I2, and A6 = I2. Explain how you know, without calculating, that A4 must be invertible.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.CR: Review Exercises
Problem 37CR
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Find an example of a 2*2 matrix such that A2 is not equal to the Identity matrix I2, A3 is not equal to I2. Explain how you konw without calculating, that A4 must be invertible.
Transcribed Image Text:Find an example of a 2 x 2 matrix A such that A? + I2, A3 + I2, and A6 = I2. Explain how
you know, without calculating, that At must be invertible.
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