Ononot — Which of the following represents the correct factorization

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Determinantshard

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Which of the following represents the correct factorization of the determinant of the $3 \times 3$ circulant matrix $C = \begin{pmatrix} x & y & z \\ z & x & y \\ y & z & x \end{pmatrix}$ , where $\omega = e^{i \frac{2\pi}{3}}$ is a primitive cube root of unity?