Please help me with this practice problem that has different parts but is only one practice problem to study for future test.

7. (a) (10 points) Let G be a group. Then we define the center of G by Z(G) = {re G| xg = gr Vg E G}. In other words, this set contains all elements commute with every other element in G. Prove Z(G) is a normal subgroup of G. (b) (5 points) List all of the elements in Z(D4), the center of DA