a). When looking at a non-zero element $c$ $\in \mathbb Z_n$ that contains inverses, what is it's relationship with $n$?
b). Also, looking at a non-zero element $c$ $\in \mathbb Z_n$ that does not contains inverses, what is it's relationship with $n$?
I know it has something to do with prime numbers and factorization.
Any help would be delightful.
EDIT: After looking at it, is it true that a). $gcd(z,n) = 1$
b). $gcd(z,n) > 1$