Let G be a group

if the order(g) = 2 for all g then prove G is abelian

My proof:

order(g) = 2

g^2 = e

g.g(^-1) = e

g.g = g.g(^-1)

therefore g= g^-1

g.g(^-1) = g^2 = e = g(^-1).g

therefore G is abelian

my proof is dont look right

HELP PLEASE!!!