Divisors of zero in a commutative ring

Let $A\neq\{0\}$ be a commutative ring and $D:=\{a\in A/ \exists x \in A\backslash\{0\}, ax=0\}$ be the set of all divisors of zero.

Show that $D$ is never empty. We now assume that $D$ contains $n\geqslant 2$ elements.
Show that $A$ contains at most $n^{2}$ elements.
Show that for any prime $n$ , there exists a ring $A$ containing $n$ divisors of zero and $n^{2}$ elements.

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