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2. Let A M, (R) be given. (a) If AA¹ On, prove that A-0₁. Does this hold if A € M₁(C)? (b) Suppose that A'AAA'. Prove that A'A= A² if and only if A is symmetric.

2. Let A M, (R) be given. (a) If AA¹ On, prove that A-0₁. Does this hold if A € M₁(C)? (b) Suppose that A'AAA'. Prove that A'A= A² if and only if A is symmetric.

Linear Algebra: A Modern Introduction
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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2. Let A € M, (R) be given. (a) If AA = 0, prove that A = 0₁. Does this hold if A € M₂, (C)? (b) Suppose that AA = AA. Prove that A'A = A² if and only if A is symmetric. 2
Transcribed Image Text:2. Let A € M, (R) be given. (a) If AA = 0, prove that A = 0₁. Does this hold if A € M₂, (C)? (b) Suppose that AA = AA. Prove that A'A = A² if and only if A is symmetric. 2
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