Thread: a certain group as 12 elements

A certain group has twelve elements:
e, ρ, ρ^2, ρ^3, ρ^4, ρ^5
R, ρR, ρ^2R, ρ^3R, ρ^4R, ρ^5R.

They satisfy the three equations:
ρ6= e, R^2= e, Rρ = ρ^5R.

Using just the equations above, show that Rρ^3= ρ^3R.

I can see that