Modulo Addition/Cayley Table

The additive group of integers modulo $m$ can be described by showing its Cayley table.

This one is for the modulo $6$:


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

\left({\Z_6, +_6}\right) & \left[\!\left[{0}\right]\!\right]_6 & \left[\!\left[{1}\right]\!\right]_6 & \left[\!\left[{2}\right]\!\right]_6 & \left[\!\left[{3}\right]\!\right]_6 & \left[\!\left[{4}\right]\!\right]_6 & \left[\!\left[{5}\right]\!\right]_6 \\ \hline \left[\!\left[{0}\right]\!\right]_6 & \left[\!\left[{0}\right]\!\right]_6 & \left[\!\left[{1}\right]\!\right]_6 & \left[\!\left[{2}\right]\!\right]_6 & \left[\!\left[{3}\right]\!\right]_6 & \left[\!\left[{4}\right]\!\right]_6 & \left[\!\left[{5}\right]\!\right]_6 \\ \left[\!\left[{1}\right]\!\right]_6 & \left[\!\left[{1}\right]\!\right]_6 & \left[\!\left[{2}\right]\!\right]_6 & \left[\!\left[{3}\right]\!\right]_6 & \left[\!\left[{4}\right]\!\right]_6 & \left[\!\left[{5}\right]\!\right]_6 & \left[\!\left[{0}\right]\!\right]_6 \\ \left[\!\left[{2}\right]\!\right]_6 & \left[\!\left[{2}\right]\!\right]_6 & \left[\!\left[{3}\right]\!\right]_6 & \left[\!\left[{4}\right]\!\right]_6 & \left[\!\left[{5}\right]\!\right]_6 & \left[\!\left[{0}\right]\!\right]_6 & \left[\!\left[{1}\right]\!\right]_6 \\ \left[\!\left[{3}\right]\!\right]_6 & \left[\!\left[{3}\right]\!\right]_6 & \left[\!\left[{4}\right]\!\right]_6 & \left[\!\left[{5}\right]\!\right]_6 & \left[\!\left[{0}\right]\!\right]_6 & \left[\!\left[{1}\right]\!\right]_6 & \left[\!\left[{2}\right]\!\right]_6 \\ \left[\!\left[{4}\right]\!\right]_6 & \left[\!\left[{4}\right]\!\right]_6 & \left[\!\left[{5}\right]\!\right]_6 & \left[\!\left[{0}\right]\!\right]_6 & \left[\!\left[{1}\right]\!\right]_6 & \left[\!\left[{2}\right]\!\right]_6 & \left[\!\left[{3}\right]\!\right]_6 \\ \left[\!\left[{5}\right]\!\right]_6 & \left[\!\left[{5}\right]\!\right]_6 & \left[\!\left[{0}\right]\!\right]_6 & \left[\!\left[{1}\right]\!\right]_6 & \left[\!\left[{2}\right]\!\right]_6 & \left[\!\left[{3}\right]\!\right]_6 & \left[\!\left[{4}\right]\!\right]_6 \\ \end{array}$