2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100912We present a matrix-based algorithm for deciding if the parametrization of a curve or a surface is invertible or not, and for computing the inverse of the parametrization if it exists.12 pages, latex, revised version accepted for publication in the Journal AAECCCommutative AlgebraAlgebraic Geometry14Q10A matrix-based approach to properness and inversion problems for rational surfacestext