Past exam of the mathematics course of the University of Cambridge / 2019 / ib / Paper 4 / 11G / c / Solution

There aresuch conjugacy classes. Every matrix in $G{L}_{10}(\mathbb{Q})$ is an invertible matrix, so by the minimal polynomial of an invertible matrix its minimal polynomial must have nonzero constant term. Buthas constant term zero and cannot be the minimal polynomial of an invertible matrix.