I would like to show that $\left(\begin{array}{ccc} 1 & s & s^2 \\ 1 & t & t^2 \\ 1 & u & u^2 \end{array}\right)$ has an inverse provided $s$, $t$ and $u$ are distinct.
I have tried to prove $A\cdot B\times C \neq 0$ without success.
I computed $A\cdot B\times C = tu^2-ut^2+st^2-su^2+s^2u-s^2t$. What to do next ?