Group of Gaussian Integer Units/Cayley Table

Cayley Table for Group of Gaussian Integer Units
The group of Gaussian integer units:
 * $\struct {U_\C, \times}$

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

\times & 1 & i & -1 & -i \\ \hline 1 & 1 & i & -1 & -i \\ i & i & -1 & -i & 1 \\ -1 & -1 & -i & 1 & i \\ -i & -i & 1 & i & -1 \\ \end{array}$