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 \(|\begin{bmatrix} 1 & x & x^2 \\ x^2 & 1 & x \\ x & x^2 & 1 \end{bmatrix}| = (1 - x^3)^2\), we will use properties of determinants.

### Step-by-step Solution:

1. **Write the Determinant**:
We start with the determinant:
\[
D = \begin{vmatrix} 1 & x & x^2 \\ x^2 & 1 & x \\ x & x^2 & 1 \end{vmatrix}
...