Multiplicative Group of Reduced Residues Modulo 8/Cayley Table

Cayley Table for Multiplicative Group of Reduced Residues Modulo 8
The multiplicative group of reduced residues modulo $8$:
 * $\Z'_8 = \left\{ {\left[\!\left[{1}\right]\!\right]_8, \left[\!\left[{3}\right]\!\right]_8, \left[\!\left[{5}\right]\!\right]_8, \left[\!\left[{7}\right]\!\right]_8}\right\}$

can be described completely by showing its Cayley table:
 * $\begin{array}{r|rrrr}

\times_8 & \left[\!\left[{1}\right]\!\right]_8 & \left[\!\left[{3}\right]\!\right]_8 & \left[\!\left[{5}\right]\!\right]_8 & \left[\!\left[{7}\right]\!\right]_8 \\ \hline \left[\!\left[{1}\right]\!\right]_8 & \left[\!\left[{1}\right]\!\right]_8 & \left[\!\left[{3}\right]\!\right]_8 & \left[\!\left[{5}\right]\!\right]_8 & \left[\!\left[{7}\right]\!\right]_8 \\ \left[\!\left[{3}\right]\!\right]_8 & \left[\!\left[{3}\right]\!\right]_8 & \left[\!\left[{1}\right]\!\right]_8 & \left[\!\left[{7}\right]\!\right]_8 & \left[\!\left[{5}\right]\!\right]_8 \\ \left[\!\left[{5}\right]\!\right]_8 & \left[\!\left[{5}\right]\!\right]_8 & \left[\!\left[{7}\right]\!\right]_8 & \left[\!\left[{1}\right]\!\right]_8 & \left[\!\left[{3}\right]\!\right]_8 \\ \left[\!\left[{7}\right]\!\right]_8 & \left[\!\left[{7}\right]\!\right]_8 & \left[\!\left[{5}\right]\!\right]_8 & \left[\!\left[{3}\right]\!\right]_8 & \left[\!\left[{1}\right]\!\right]_8 \\ \end{array}$