2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71487We show that with any finite partially ordered set one can associate a matrix whose determinant factors nicely. As corollaries, we obtain a number of results in the literature about GCD matrices and their relatives. Our main theorem is proved combinatorially using nonintersecting paths in a directed graph.10 pages, see related papers at http://www.math.msu.edu/~saganCombinatorics11C20 (Primary) 05E99, 11A25, 15A36 (Secondary)text