G - Finite Group

T - Automorphism of G

For all x in G, T(x) = xIFFx=1

Also, T(T(x))=x for all x in G.

Prove G is abelian.

Struggling a lot with this. I suspect .

And once I establish this, proving G is abelian is simple.

But not going anywhere with the hunch of .

Any pointers please?