Q: if $R$ is a ring such that for every $x\in R$ , $x^4=x$, then prove $R$ is commutative.
What I've tried: First we notice that $-x=(-x)^4=x^4=x$.
$x+x=2x=0$
Then we can show that $x^2+x$ is is a central because $(x^2+x)^2=x^4+2x^3+x^2=x^2+x$
($x^2+x$ is idempotent)
Now I can't proceed from here. :( Any help is much appreciated!
