If ab=0 what is the possible integer value of a and b?

If $ab=0$ what is the possible integer value of $a$ and $b$.

Answer 

The only zero divisor in the Ring of integers is zero. Hence the simplest answer to this question is $ab=0$ implies $a=0$ and $b=0$.

Although, there are other Rings with non-zero divisors e.g $3$ and $4$ are zero divisors in the clock arithmetic of $\mathbb{Z}/12\mathbb{Z}$ because $3\times{4}=0(mod 12)$.