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

Answered: Image /qna-images/answer/ba30f8fb-5e26-43b1-b8f0-bb79d38c0e04.jpg

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.

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.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...

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