Consider (S, +,•),where S is a set and + and • are binary operations on S such that 

(S, +) is a group, 

(S^*, •) is a group where S^* consists of all elements of S except the additive identity element, 

a(b + c) =(ab)+ (ac) and (a+ b)c = (ac) + (be) for all a, b, c ∈ S. Show that (S, +, •) is a division ring.