22 Let A, B E Mnxn (F). We say that A is similar to B, denoted by A B, if there exists an invertible matrix Q € Mnxn(F) such that A = Q-¹BQ. Prove the following statements. (a) A~ A for any A € Mnxn (F). (b) If A, B E Mnxn (F) and A ~B, then B~ A. (c) If A, B, C = Mnxn (F) and A ~ B and B~ C, then A~ C.

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Q: Suppose A is a symmetric matrix. (Au)" : u"A

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Q: 34. Is it possible for A³ to be an identity matrix without A being invertible? Explain.

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Q: -1 [A] = 4 3 -3 2 %3D L3 1] 2.

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