  In a recent paper of the author with D. Dummit and H. Kisilevsky, we
constructed a collection of matrices defined by quadratic residue symbols,
termed "quadratic residue matrices", associated to the splitting behavior of
prime ideals in a composite of quadratic extensions of $\mathbb{Q}$, and proved
a simple criterion characterizing such matrices. We then analyzed the analogous
classes of matrices constructed from the cubic and quartic residue symbols for
a set of prime ideals of $\mathbb{Q}(\sqrt{-3})$ and $\mathbb{Q}(i)$,
respectively. In this paper, the goal is to construct and study the
finite-field analogues of these residue matrices, the "$d$th-power residue
matrices", using the general $d$th-power residue symbol over a finite field.
