Ononot — Let C = \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0

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Eigenvalues & Eigenvectorshard

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Let $C = \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{pmatrix}$ be a $3 \times 3$ permutation matrix representing a cyclic shift. If $\omega = e^{\frac{2\pi i}{3}}$ , what are the eigenvalues of $C$ ?