By using properties of determinants. Show that:`|[1,x,x^2],[x^2, 1,x],[x,x^2, 1]|=(1-x^3)^2`

Explanation

To show that the determinant

\[
D = \begin{vmatrix}
1 & x & x^2 \\
x^2 & 1 & x \\
x & x^2 & 1
\end{vmatrix}
...