G is a group all of whose elements have order two: a^2=1, prove that it is abelian.
Please can you help me with this question?
Let G be a group all of whose elements have order two: a^2=1 for every aEG.
(i) Prove that G is abelian
(ii) If G is finite, prove its order is of power of two.
I know that abelian is another way of saying commutative, which I understand this as being when you apply a group operation to two group elements, that the result does not depend on its order.
However, I do not understand how to apply this to my question, and do not understand where a^2=1 will come into it (unless obviously its for part (ii)).
I don't know where to begin on part(ii) and are unsure if part (i) will help me with this.
Any help will be great