A be an nxn matrix such that det A=1. Show that 1) 1 is an eigenvalue of A if and only if 1 is an eigenvalue of A^-1

Elementary Linear Algebra (MindTap Course List)
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ISBN:9781305658004
Author:Ron Larson
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Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 55E
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Let A be an nxn matrix such that det A=1. Show that

1) 1 is an eigenvalue of A if and only if 1 is an eigenvalue of A^-1

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