This is for abstract algebra class. Please show me all the details from scratch.

6. (a) Show that every group G with identity e and such that =+ z = e for all x G is abelian. (b) Let G be a group with a finite number of elements. Show that for any a G, there exists an n N such that a" = e. () Show that if (a*b)? = a *b? for a and b in a group G, then a*b = b+ a. [Note that this is not saying that G is abelian.]