If `S_n = \alpha^n+\beta^n+\gamma^n` then show that $ \begin{vmatrix} S_0 & S_1 & S_2 \\ S_1 & S_2 & S_3 \\ S_2 & S_3 & S_4 \end{vmatrix} = (\alpha-\beta)^2 (\beta-\gamma)^2 (\gamma-\alpha)^2 $