Let a, b e G such that a and b commute, i.e. ab = ba. Note that we are not claiming G is abelian. Prove that the following commute. (a) a-l and b-1 (b) a and b-1 (c) a and ab (d) a? and b2 (e) xax- and xbx- for any x e G

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.4: Complex And Rational Zeros Of Polynomials
Problem 45E
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Let a, b e G such that a and b commute, i.e. ab
ba. Note that we are not claiming G is
abelian. Prove that the following commute.
(a) a-1 and b-1
(b) a and b-1
(c) a and ab
(d) a? and b?
(e) xax-1 and xbx-1 for any x e G
Transcribed Image Text:Let a, b e G such that a and b commute, i.e. ab ba. Note that we are not claiming G is abelian. Prove that the following commute. (a) a-1 and b-1 (b) a and b-1 (c) a and ab (d) a? and b? (e) xax-1 and xbx-1 for any x e G
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