Let ∗:G×G→G be an associative binary operation on the set G such that (G2R) There is an element e∈G such that, for all a∈G a∗e=a. (G3R) To each a∈G there is an a
ˉ
∈G such that a∗ a
ˉ
=e Show that (G,∗) is a group. This shows that axioms (G2R), (G3R) and (G1) together imply (G1), (G2) and (G3).