Using properties of determinants prove that:

Using properties of determinants prove that:

$\left|\begin{array}{lll}x-3 & x-4 & x-\alpha \\ x-2 & x-3 & x-\beta \\ x-1 & x-2 & x-\gamma\end{array}\right|=0$, where $\alpha, \beta, y$ are in AP.