Using properties of determinants, prove the following: `|[1,x,x^2],[x^2, 1,x],[x,x^2,1]|=(1-x^3)^2`

Explanation

To prove that

\[
\left| \begin{array}{ccc}
1 & x & x^2 \\
x^2 & 1 & x \\
x & x^2 & 1
\end{array} \right| = (1 - x^3)^2,
...