Let G be a group and let g,hinG. The commutator of g and h is the group element
g,h given by
[g,h]=ghg^(-1)h^(-1).
(a) Show that [g,h]^(-1)=[h,g].
(b) Show that G is abelian if and only if [g,h]=e for all g,hinG.
4. Let G be a group and let g,h e G. The commutator of g and h is the group element [g, h] given by [g,h]=ghg-1h-1
(a) Show that [g,h]-1=[h,g]
(b) Show that G is abelian if and only if [g,h] = e for all g,h e G.
