  We compute the exact Fourier dimension of the set of $\Psi$-well-approximable
$m \times n$ matrices (and the set of $\Psi$-well-approximable numbers) in the
homogeneous and inhomogeneous cases for any approximation function $\Psi$
satisfying $\sum_{q \in \mathbb{Z}^n} \Psi(q)^m < \infty$.
