Referring to Exercise 36, show that H ={ a | a G} is a subgroup

Referring to Exercise 36, show that H ={ γ_a | a ∈ G} is a subgroup of S_G, the group of all permutations of G. 

Data from Exercise 36

Let G be a group and let a be a fixed element of G. Show that the map γ_a : G → G, given by γ_a (g) = ag for g ∈ G, is a permutation of the set G.