  Maximum rank-distance (MRD) codes are extremal codes in the space of $m\times
n$ matrices over a finite field, equipped with the rank metric. Up to
generalizations, the classical examples of such codes were constructed in the
1970s and are today known as Gabidulin codes. Motivated by several recent
approaches to construct MRD codes that are inequivalent to Gabidulin codes, we
study the equivalence issue for Gabidulin codes themselves. This shows in
particular that the family of Gabidulin codes already contains a huge subset of
MRD codes that are pairwise inequivalent, provided that $2\le m\le n-2$.
