Consider the homomorphism
`f: ZZ_p ^"*" rightarrow ZZ_p ^"*"` defined by `f(x) = x^2`(mod p), where p is a prime p > 2. The kernel of this homomorphism, ker(f), is the set of elements in `ZZ_p ^"*"` that are mapped to the multiplicative identity 1 (mod p). Which of the following correctly describes the elements in the kernel for p > 2:
A) ker(f) = {`x in ZZ_p ^"*" : x^2 = a` (mod p) for some quadratic residue a}.
B) ker(f) = {`x in ZZ_p ^"*" : x^2 = 1` (mod p)} ?