Let A be an n×n matrix such that det A=1. Show that (a) A. adj A=l (b) 1 is an eigenvalue of A ifand only if 1 is an eigenvalue of A ^-1
Let A be an n×n matrix such that det A=1. Show that (a) A. adj A=l (b) 1 is an eigenvalue of A ifand only if 1 is an eigenvalue of A ^-1
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 26EQ
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Question
Let A be an n×n matrix such that det A=1. Show that
(a) A. adj A=l
(b) 1 is an eigenvalue of A ifand only if 1 is an eigenvalue of A ^-1
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