This shows the Cayley for the dihedral group $D_8$, which is a Latin square. The group elements are called $r_i$ and $s_i$, and they satisfy \begin{align*} r_ir_j &= r_{i+j} & r_is_j &= s_{i+j} \\ s_ir_j &= s_{i-j} & s_is_j &= r_{i-j}. \end{align*}