Question 8 Let A be a square matrix with eigenvalue X. Prove the following implications. (a) A² = 0 λ = 0 (b) A² = A ⇒ λ = 0 or λ =1 (c) A² = I λ = 1 or λ = -1
Question 8 Let A be a square matrix with eigenvalue X. Prove the following implications. (a) A² = 0 λ = 0 (b) A² = A ⇒ λ = 0 or λ =1 (c) A² = I λ = 1 or λ = -1
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 75E
Question
![Question 8
Let A be a square matrix with eigenvalue X. Prove the following implications.
(a) A²
= 0
λ = 0
(b) A² = A ⇒ λ = 0 or λ =1
(c) A²
= I λ = 1 or λ = -1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F322742eb-4a31-4e3c-832a-7268262542b0%2Fbb49e4d6-04ce-4dd2-a566-d59b2ea7c82d%2Fmhg5j69_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 8
Let A be a square matrix with eigenvalue X. Prove the following implications.
(a) A²
= 0
λ = 0
(b) A² = A ⇒ λ = 0 or λ =1
(c) A²
= I λ = 1 or λ = -1
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