If CARD(X)≥2, Prove that A^X, which is known to be a commutative and unitary ring, is not an integral domain.

Question

Proving that A^X is not an integral domain, knowing it is already commutative and unitary in regards to standard multiplication, means that for any f,g functions of A^X (so that f and g both go from X to A), we need to demonstrate that (f•g)(x)=OA, even if f and g are not null functions. We had defined (f•g)(x) as f(x)•g(x) beforehand. I can't seem to find a way to do this and also incorporate the cardinality of X being greater or equal to 2 in the proof.