Boolean rings are commutative

#ring_theory

Suppose $R$ is a ring such that $r^{2} = r$ for every element $r \in R$ .
(a) Prove $r = - r$ for every element $r \in R$ .
(b) Show $R$ must be commutative. Hint: Consider $(a + b)^{2}$ .

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Suppose $R$ is a ring such that $r^2=r$ for every element $r\in R$.
\begin{enumerate}[label=\alph*)]
	\item Prove $r=-r$ for every element $r\in R$.
	\item Show $R$ must be commutative. {\itshape Hint:} Consider $(a+b)^2$.
\end{enumerate}