2. Let A E Mnxn(R) be an invertible matrix and let A E R. Prove that A is an eigenvalue for A if and only if is an eigenvalue for A-1. (Note: be sure to address why exists!)

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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2. Let A E Mnxn(R) be an invertible matrix and let A E R. Prove that A is an eigenvalue for A if and
only if is an eigenvalue for A-1. (Note: be sure to address why exists!)
Transcribed Image Text:2. Let A E Mnxn(R) be an invertible matrix and let A E R. Prove that A is an eigenvalue for A if and only if is an eigenvalue for A-1. (Note: be sure to address why exists!)
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