Suppose that A is a ring and I is an ideal of A. Prove that the quotient ring A/I is an integral domain if and only if I satisfies the following:

$\displaystyle I \neq A$ and $\displaystyle xy \in I \implies (x\in I$ or $\displaystyle y\in I)$.

I have tried it both ways using a contradictory argument but to no avail. Help much appreciated.