With $H = \{ \rho_{0} , \rho_{3} \}$, how would I compute $( \mu_{1} , H)(\mu_{2} , H)$ and $( \mu_{2} , H)(\mu_{1} , H)$?
I'm assuming I'd calculate $( \mu_{1} , \rho_{0} )( \mu_{2} , \rho_{3} )$ and $( \mu_{2} , \rho_{0} )( \mu_{1} , \rho_{3} )$ but I'm not sure how to get an answer. Do I combine them together? For instance $( \mu_{1} , \rho_{0}) = \mu_{1}$ and $(\mu_{2} , \rho_{3}) = \delta_{3}$. So does that mean that $( \mu_{1} , \rho_{0} )( \mu_{2} , \rho_{3} ) = (\mu_{1} , \delta_{3})$?