Really struggling on where to start with this question:

a. Let G be a group, let H be a subgroup of G and let g be a fixed element of G. Show that the subset gHg^{-1 }= {ghg^{-1}: h ϵ H} is also a subgroup of G.

b. Suppose g, x ϵ G. Show that (gxg^{-1 })^{n }=gx^{n}g^{-1 }for all n ϵ Z, and hence (or otherwise) that o(gxg-1) = o(x)

Any help would be really appreciated thanks