Group with a property that $x^{-1}=x$ Suppose that we have some group G in which the following holds for all $x $ belongs to G: $x^{-1} =x$. Prove that G is abelian.

How would you guys solve this one?
Well, we have 
$$xy = (xy)^{-1} = y^{-1}x^{-1} = yx$$ for all $x,y \in G$. Hence $G$ is abelian.
Take $x,y \in G$ , you want to show that $xy = yx$. 

Or , the commutator of $x,y$ is the identity , that is $[x,y] = xyx^{-1}y^{-1}=e$. 

Can you take this from here?