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.
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