\begin{equation*} \begin{array}{c|cccccc} \circ & \identity & \rho_1 & \rho_2 & \mu_1 & \mu_2 & \mu_3 \\ \hline \identity & \identity & \rho_1 & \rho_2 & \mu_1 & \mu_2 & \mu_3 \\ \rho_1 & \rho_1 & \rho_2 & \identity & \mu_3 & \mu_1 & \mu_2 \\ \rho_2 & \rho_2 & \identity & \rho_1 & \mu_2 & \mu_3 & \mu_1 \\ \mu_1 & \mu_1 & \mu_2 & \mu_3 & \identity & \rho_1& \rho_2\\ \mu_2 & \mu_2 & \mu_3 & \mu_1 & \rho_2 & \identity & \rho_1\\ \mu_3 & \mu_3 & \mu_1 & \mu_2 & \rho_1 & \rho_2& \identity \end{array} \end{equation*}