Given any subset [tex]H \subset G[/tex], how would you attempt to prove that it is a subgroup of [tex]G[/tex]? What properties of [tex]H[/tex] would you attempt to verify?
Well I guess associativity, unique inverse and identity element are all trivial.
What I'm having trouble with is closure, proving that for any elements a and b in the group, ab is also in the group.
You need to prove that if a and b are elements of order 2 (i.e. [itex]a^{2} = b^{2} = e[/itex]), then so is [itex]c = a b[/itex]. You need to evaluate [itex]c^{2}[/itex] and use the commutativity of the group.