If \( p, q, r \) are the cube roots of unity, then what is \( \begin{vmatrix} p^2+q^2 & r^2 & r^2 \\ p^2 & q^2+r^2 & p^2 \\ q^2 & q^2 & r^2+p^2 \end{vmatrix} \) equal to ?

Explanation

The standard expansion for this determinant is 4p^2q^2r^2. Since p, q, r are cube roots of unity (1, \omega, \omega^2), their product pqr = 1. Therefore, the determinant evaluates to 4(1)^2 = 4.

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