Proper Zero Divisor/Examples/Multiplication Modulo 6

Examples of Proper Zero Divisors
Consider the multiplicative monoid of integers modulo $6$, defined by its Cayley table:

Thus we have:
 * $\eqclass 2 6 \times \eqclass 3 6 = \eqclass 0 6$

and:
 * $\eqclass 4 6 \times \eqclass 3 6 = \eqclass 0 6$

Hence in the ring of integers modulo $6$, there are seen to be $3$ proper zero divisors: $\eqclass 2 6$, $\eqclass 3 6$ and $\eqclass 4 6$.