Let $F = \mathbb{Q}(\omega, \sqrt[3]{2})$, where $\omega \in \mathbb{C}$ is a primitive cube-root of unity. Find a $\mathbb{Q}$-basis for $F$ (with proof). Let $\mu : F \longrightarrow F$ be the $\mathbb{Q}$-linear map given by $\mu(a) = \omega^2 a$. Find the matrix of $\mu$ with respect to the basis obtained above.