1. Abelian

Suppose that His a group in which x^2= e for all x in H.
Prove that H
is Abelian.

Thanks

2. consider $x,y \in G$

then consider $(xy)^2$ and $x^ 2y^2$
$
(xy)^2 = xyxy = e$

$x^2y^2 = xxyy = e$
$\Rightarrow xyxy = xxyy$
Now use properties of Groups to show why the above equation implies that G is Abelian