elementary number theory - Congruence relationships.

I need to prove (or disprove but I don't think that's the case) that:

if $ab \equiv 0$ (mod $n$), then $ a\equiv 0$ (mod $n$) or $b\equiv0$ (mod $n$)

I know that $ab\equiv 0$ (mod $n$) $\Longleftrightarrow n|ab$, so if that's true then n must divide either a or b but I don't know how to prove it.

Any assistance is much appreciated.