Prove that if AT A = A, then A is symmetric and A = A².

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.2: Matrix Algebra
Problem 21EQ: Prove the half of Theorem 3.3 (e) that was not proved in the text.
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Prove that if AT A = A, then A is symmetric and A = A².
Transcribed Image Text:Prove that if AT A = A, then A is symmetric and A = A².
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