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We consider separately radial (with corresponding group ${𝕋}^n$) and radial (with corresponding group $\mathrm{U}\left(n\right))$ symbols on the projective space ${\mathbb{P}}^n\left(ℂ\right)$, as well as the associated Toeplitz operators on the weighted Bergman spaces. It is known that the $C^{*}$-algebras generated by each family of such Toeplitz operators are commutative (see R. Quiroga-Barranco and A. Sanchez-Nungaray (2011)). We present a new representation theoretic proof of such commutativity. Our method is easier and more enlightening as it shows that the...