Let $G$ be a finite semigroup .Prove that there exist $x\in G $ such that $x^2=x$

Question

Let $G$ be a finite semigroup .Prove that there exist $x\in G $ such that $x^2=x$

How to approach this problem.i know i have to use that $G$ is finite set. but from where to start. please provide any hint where to start with ??

Answer 1

Assume there isn't such an element. What happens for $x^{2n}$, $n\in \mathbb{N}$?