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Thanks a bunch InteGrand!

I thought about using the identity and inverse axioms but I couldn't get anywhere with them. I thought that it would be straight forward that ab = e since there are only 3 elements in G, so either a = b^{-1} or b = a^{-1} . But I was confused when I saw that part b said a^2 = b because...

Hopefully you don't mind if i post a question here. (taking MATH2601 this semester) Suppose that G is a group with precisely three distinct elements e (the identity), a and b. a) Prove that ab = e (Hint: eliminate other possibilities). b) Prove that a^2 = b. c) Deduce that G = {e, a, a^2}...

Sign me up too :)