Action of projections on Banach algebras

Let $\mathcal{A}$ be a Banach algebra and $n>1$, a fixed integer. The main objective of this paper is to talk about the commutativity of Banach algebras via its projections. Precisely, we prove that if $\mathcal{A}$ is a prime Banach algebra admitting a continuous projection $\mathcal{P}$ with image in $\mathcal{Z}(\mathcal{A})$ such that $\mathcal{P}(a^n)=a^n\text{for all}a\in \mathcal{G}$, the nonvoid open subset of $\mathcal{A}$, then $\mathcal{A}$ is commutative and $\mathcal{P}$ is the identity mapping on $\mathcal{A}$. Apart from proving some other results, as an application we prove that, a normed algebra is commutative iff the interior of its center is non-empty. Furthermore, we provide some examples to show that the assumed restrictions cannot be relaxed. Finally, we conclude our paper with a direction for further research.