If w is the imaginary cube root of unity evaluate
`|(1,w,w^2),(w,w^2,1),(w^2,1,w)|`

Explanation

To evaluate the determinant \( D = \begin{vmatrix} 1 & \omega & \omega^2 \\ \omega & \omega^2 & 1 \\ \omega^2 & 1 & \omega \end{vmatrix} \), where \( \omega \) is the imaginary cube root of unity, we can follow these steps:

### Step 1: Write down the determinant
We start with the determinant:
\[ D = \begin{vmatrix} 1 & \omega & \omega^2 \\ \omega & \omega^2 & 1 \\ \omega^2 & 1 & \omega \end{vmatrix} \]

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