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Show that the ring is commutative?

Given ring $(R, +, \cdot)$ $(R,+,*)$ with $x^{3} = x$ $x^3=x$ ,

$\forall$ $AA$ $x$ $x$ $\in$ $in$ $R$ $R$

Show that the ring is commutative?

1 Answer

Vinícius Ferraz

May 24, 2018

see below

Explanation:

$x x x = x$ $x x x = x$
$x x = e$ $x x = e$
$x = x^{- 1}$ $x = x^-1$

$x y = {(x y)}^{- 1} = y^{- 1} x^{- 1} = y x$ $xy = (xy)^-1 = y^-1x^-1 = yx$

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