Prove that the equation $x^2=x$ has the same solutions in rational numbers as in integers

Question

I was wondering if you could help me start in my discrete math homework. I'm asked to prove that A = B:

$A =\{x \in \mathbb{Z}\mid x^2 = x\}$ and $B = \{x \in \mathbb{Q}\mid x^2 = x\}$

I'm having problems as to where to start and I wanted to know where to begin this problem.

Answer 1

HINT: rewrite it in the form $$x(x-1)=0$$