Given a finite group $G$, prove that the matrices of its right-regular representation, defined according to Eq. (3.73), obey the group multiplication law, i.e., $R(g) R\left(g^{\prime}\right)=R\left(g g^{\prime}\right)$. Prove also that this would not be true, if in Eq. (3.73) one had defined $ho_{g}(h)=h g$ instead of $ho_{g}(h)=h g^{-1}$.

Data from Eq. 3.73

Transcribed Image Text:

h Rg(h) = hg.