Modulo Multiplication/Cayley Table/Modulo 3

Cayley Table for Modulo Multiplication

The multiplicative monoid of integers modulo $m$ can be described by showing its Cayley table.

This one is for modulo $3$:

$\begin {array} {r|rrr} \struct {\Z_3, \times_3} & \eqclass 0 3 & \eqclass 1 3 & \eqclass 2 3 & \\ \hline \eqclass 0 3 & \eqclass 0 3 & \eqclass 0 3 & \eqclass 0 3\\\eqclass 1 3 & \eqclass 0 3 & \eqclass 1 3 & \eqclass 2 3 \\ \eqclass 2 3 & \eqclass 0 3 & \eqclass 2 3 & \eqclass 1 3 \\ \end {array}$

which can also be presented:

$\begin {array} {r|rrrrr} \times_3 & 0 & 1 & 2 \\ \hline 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 2 \\ 2 & 0 & 2 & 1 \end {array}$