Modulo Multiplication/Cayley Table

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 $6$:


 * $\begin{array}{r|rrrrrr}

\struct {\Z_6, \times_6} & \eqclass 0 m & \eqclass 1 m & \eqclass 2 m & \eqclass 3 m & \eqclass 4 m & \eqclass 5 m \\ \hline \eqclass 0 m & \eqclass 0 m & \eqclass 0 m & \eqclass 0 m & \eqclass 0 m & \eqclass 0 m & \eqclass 0 m \\ \eqclass 1 m & \eqclass 0 m & \eqclass 1 m & \eqclass 2 m & \eqclass 3 m & \eqclass 4 m & \eqclass 5 m \\ \eqclass 2 m & \eqclass 0 m & \eqclass 2 m & \eqclass 4 m & \eqclass 0 m & \eqclass 2 m & \eqclass 4 m \\ \eqclass 3 m & \eqclass 0 m & \eqclass 3 m & \eqclass 0 m & \eqclass 3 m & \eqclass 0 m & \eqclass 3 m \\ \eqclass 4 m & \eqclass 0 m & \eqclass 4 m & \eqclass 2 m & \eqclass 0 m & \eqclass 4 m & \eqclass 2 m \\ \eqclass 5 m & \eqclass 0 m & \eqclass 5 m & \eqclass 4 m & \eqclass 3 m & \eqclass 2 m & \eqclass 1 m \\ \end{array}$

which can also be presented:


 * $\begin{array}{r|rrrrrr}

\times_6 & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 2 & 3 & 4 & 5 \\ 2 & 0 & 2 & 4 & 0 & 2 & 4 \\ 3 & 0 & 3 & 0 & 3 & 0 & 3 \\ 4 & 0 & 4 & 2 & 0 & 4 & 2 \\ 5 & 0 & 5 & 4 & 3 & 2 & 1 \\ \end{array}$