Let G1 and G2 be two groups (written multiplicatively) and let f: Gı-\ G2 be an isomorphism (i) Show that f(1)-1 (here the first 1 is the identity in Gi and the second 1 is the identity in Gı). (ii) Show that, for all g E Ģı, f(g-1-(f(g)) (iii) Let H be a subset of G1. Show that, if H is a subgroup of ĢI then f(H) is a subgroup of G2. By applying this result to the inverse isomorphism f-1: G2 -» Gi, show that H is a subgroup of Gif(H) is a subgroup of G2.