I want to show that the elements of under multiplication that have inverses are also the generators of under addition.

My answer so far: The only integers with multiplicative inverses are -1 and 1; and these are generators of ( ).

I feel like this answer is too simple though... Can I show this more rigorously? Besides saying that (obviously) the gcd(1,n)=1, and =(1)x, =(-1)x, generates ? Or am I interpreting this question completely wrong?