Throughout the rest of the problem, we fix an odd integer $\ell \geq 3$ and $q$ a primitive $\ell$-th root of unity. Show that $q^2$ is a primitive $\ell$-th root of unity.
Throughout the rest of the problem, we fix an odd integer $\ell \geq 3$ and $q$ a primitive $\ell$-th root of unity. Show that $q^2$ is a primitive $\ell$-th root of unity.