$R$ is an associative ring with no zero divisors that has an element $a\neq 0$, such that $a*a=a$. Prove $a$ is the identity element of $R$

Question

Let $R(+,*)$ be an associative ring with no zero divisors that has an element $a\neq 0$, such that $a*a=a$. Prove that $a$ is the multiplicative identity element of $R$.

I found similar questions posted here, but none of them had $a*a=a$.

Any hints?

Answer 1

Hint: $a*(ax-x)=0 $