(\(R,+\),.) commutative ring and \(\displaystyle{a}\in{R}\)

Such that a is idempotenr element

i.e \(\displaystyle{a}^{{2}}={a}\)

\(\displaystyle{\left({1}-{a}\right)}^{{2}}={\left({1}-{a}\right)}{\left({1}-{a}\right)}\)

\(\displaystyle={1}-{a}-{a}+{2}^{{2}}\)

\(\displaystyle={1}-{2}{a}+{a}{\left\lbrace{\sin{{c}}}{e}{a}^{{2}}={a}\right\rbrace}\)

\(\displaystyle={1}-{a}\)

\(\displaystyle\Rightarrow{\left({1}-{a}\right)}^{{2}}={1}-{a}\)

\(\displaystyle\Rightarrow\) \(1-a\) is idempotent element