Question

is D3 abelian?If no then why?explain

Answer 1

D3 is non-abelian (or)noncommutative group..in equilateral triangle ABC.. //R(A) = B; R(B) = C; R(C) = A//(R- is the rotation) ...//r(A) = A; r(B) = C; r(C) = B//(r- is the reflection) finding the R; r by D3; R∘r(A) = B and r∘R(A) = C, so R∘r ≠ r∘R( you have see the eq.triangle rotation and reflation respective to the axis), thus this equation represent the s3 or D3 is a non-abelian.