How can I prove that $ \begin{vmatrix} \frac{1}{(x_1-y_1)^2} & \frac{1}{(x_1-y_2)^2} & \cdots & \frac{1}{(x_1-y_n)^2} \\ \frac{1}{(x_2-y_1)^2} & \frac{1}{(x_2-y_2)^2} & \cdots & \frac{1}{(x_2-y_n)^2} \\ \vdots & \vdots & \ddots & \vdots \\ \frac{1}{(x_n-y_1)^2} & \frac{1}{(x_n-y_2)^2} & \cdots & \frac{1}{(x_n-y_n)^2} \end{vmatrix} \ne 0 $?
For $x_i$ and $y_i$ are all distinct.