Dihedral Group D3/Cayley Table

Cayley Table of Dihedral Group $D_3$
The Cayley table of the dihedral group $D_3$ can be written:
 * $\begin{array}{c|cccccc}

& e    & a     & a^2   & b     & a b   & a^2 b \\ \hline e    & e     & a     & a^2   & b     & a b   & a^2 b \\ a    & a     & a^2   & e     & a b   & a^2 b & b     \\ a^2  & a^2   & e     & a     & a^2 b & b     & a b   \\ b    & b     & a^2 b & a b   & e     & a^2   & a     \\ a b  & a b   & b     & a^2 b & a     & e     & a^2   \\ a^2 b & a^2 b & a b  & b     & a^2   & a     & e     \\ \end{array}$

where the group presentation of $D_3$ is given as: