Prove that $\dim_\mathbb{C}(M)$ is finite for simple right $A$-module $M$ where $A$ is a finite dimensional $\mathbb{C}$-algebra

Question

Let $A$ be a finite dimensional $\mathbb{C}$-algebra and let $M$ be a simple right $A$-module. Show that $\dim_\mathbb{C}(M)$ is finite.

This is a part of practice question [Algebra I. Martin Isaacs 12.19] that I don't understand. Can anyone explain me why this is true?