3. Let A, B € Mnxn (F) be n x n matrices. (a) Prove that tr(A + B) = tr(A) + tr(B). (b) Prove that tr(AB) = tr(BA). (c) If A and B are similar n × n matrices, prove that tr(A) = tr(B).
3. Let A, B € Mnxn (F) be n x n matrices. (a) Prove that tr(A + B) = tr(A) + tr(B). (b) Prove that tr(AB) = tr(BA). (c) If A and B are similar n × n matrices, prove that tr(A) = tr(B).
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.5: Determinants
Problem 82E: Use an example chosen from 22 matrices to show that for nn matrices A and B,ABBA but AB=BA.
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