Modulo Addition/Cayley Table/Modulo 4

Cayley Table for Addition Modulo $4$
The additive group of integers modulo $4$ can be described by showing its Cayley table:
 * $\begin{array}{r|rrrr}

\left({\Z_4, +_4}\right) & \left[\!\left[{0}\right]\!\right]_4 & \left[\!\left[{1}\right]\!\right]_4 & \left[\!\left[{2}\right]\!\right]_4 & \left[\!\left[{3}\right]\!\right]_4 \\ \hline \left[\!\left[{0}\right]\!\right]_4 & \left[\!\left[{0}\right]\!\right]_4 & \left[\!\left[{1}\right]\!\right]_4 & \left[\!\left[{2}\right]\!\right]_4 & \left[\!\left[{3}\right]\!\right]_4 \\ \left[\!\left[{1}\right]\!\right]_4 & \left[\!\left[{1}\right]\!\right]_4 & \left[\!\left[{2}\right]\!\right]_4 & \left[\!\left[{3}\right]\!\right]_4 & \left[\!\left[{0}\right]\!\right]_4 \\ \left[\!\left[{2}\right]\!\right]_4 & \left[\!\left[{2}\right]\!\right]_4 & \left[\!\left[{3}\right]\!\right]_4 & \left[\!\left[{0}\right]\!\right]_4 & \left[\!\left[{1}\right]\!\right]_4 \\ \left[\!\left[{3}\right]\!\right]_4 & \left[\!\left[{3}\right]\!\right]_4 & \left[\!\left[{0}\right]\!\right]_4 & \left[\!\left[{1}\right]\!\right]_4 & \left[\!\left[{2}\right]\!\right]_4 \\ \end{array}$

It can also be presented:


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

+_4 & 0 & 1 & 2 & 3 \\ \hline 0 & 0 & 1 & 2 & 3 \\ 1 & 1 & 2 & 3 & 0 \\ 2 & 2 & 3 & 0 & 1 \\ 3 & 3 & 0 & 1 & 2 \\ \end{array}$