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=teps) Given that, (G, *) be To a group such that x² = e = x&G. show that (G, *) is abelian group. i-e to show that xxy = y****, YEG

=teps) Given that, (G, *) be To a group such that x² = e = x&G. show that (G, *) is abelian group. i-e to show that xxy = y****, YEG

Advanced Engineering Mathematics
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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I don't understand why the inverse is x=x^-1 when the binary operation is not multiplication. Please explain it to me. Thank you 

steps) Given that, (G, *) be To -group such that x² = e = x= G. show that (G₁+) is abelian group. ie to show that x*y = y**** YEG JL r
Transcribed Image Text:steps) Given that, (G, *) be To -group such that x² = e = x= G. show that (G₁+) is abelian group. ie to show that x*y = y**** YEG JL r
sty I! solution As given x² = e Ұ нест xxl=e X XEG Now = x= x² + i-e inverse of x itself. let a, b = G = a²=e & b² = e Also axb E G ( By clasure property of G) cor (axb)' = axb (as (a*b)² = a*b → inverse of (a*b) = a*b. = a*b) A (axb) = .. Now, (a*b) 9*b = b* = (b*a)' = b* a .: G is = axb ахь = бжа ba x & G x is ( as (b*0²) = bxa). съжал 9₁ b € G. # an abelian group.
Transcribed Image Text:sty I! solution As given x² = e Ұ нест xxl=e X XEG Now = x= x² + i-e inverse of x itself. let a, b = G = a²=e & b² = e Also axb E G ( By clasure property of G) cor (axb)' = axb (as (a*b)² = a*b → inverse of (a*b) = a*b. = a*b) A (axb) = .. Now, (a*b) 9*b = b* = (b*a)' = b* a .: G is = axb ахь = бжа ba x & G x is ( as (b*0²) = bxa). съжал 9₁ b € G. # an abelian group.
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