2. Let A € M₂ (R) be given. (a) If AA¹ = 0, prove that A = On. Does this hold if A € M₁ (C)? (b) Suppose that A'A= AA. Prove that AA = A² if and only if A is symmetric.
2. Let A € M₂ (R) be given. (a) If AA¹ = 0, prove that A = On. Does this hold if A € M₁ (C)? (b) Suppose that A'A= AA. Prove that AA = A² if and only if A is symmetric.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Help me answer question number 2
Transcribed Image Text:2.
Let A € M₂ (R) be given.
(a) If AA¹
=
= On, prove that A = 0₁. Does this hold if A € M₂, (C)?
(b) Suppose that AA = AA. Prove that AA = A² if and only if A is symmetric.
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