$\alpha ,\beta ,\gamma$ are the root of $x^3-2x^2-x+2=0$. Centroid of triangle with verties $\left(\alpha ,\beta ,\gamma \right)$, $(\beta ,\gamma ,\alpha ),(\gamma ,\alpha ,\beta )$ is

• A

  $\left(-\frac{{\displaystyle 2}}{{\displaystyle 3}},\frac{{\displaystyle 2}}{{\displaystyle 3}},-\frac{{\displaystyle 2}}{{\displaystyle 3}}\right)$

• B

  $\left(-\frac{{\displaystyle 2}}{{\displaystyle 3}},\frac{{\displaystyle 1}}{{\displaystyle 3}},\frac{{\displaystyle 2}}{{\displaystyle 3}}\right)$

• C

  $\left(\frac{2}{3},\frac{2}{3},\frac{2}{3}\right)$

• D

  $\left(\frac{{\displaystyle 4}}{{\displaystyle 3}},\frac{{\displaystyle 2}}{{\displaystyle 3}},\frac{{\displaystyle 2}}{{\displaystyle 3}}\right)$