2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167044Random matrices arise in many mathematical contexts, and it is natural to ask about the properties that such matrices satisfy. If we choose a matrix with integer entries at random, for example, what is the probability that it will have a particular integer as an eigenvalue, or an integer eigenvalue at all? If we choose a matrix with real entries at random, what is the probability that it will have a real eigenvalue in a particular interval? The purpose of this paper is to resolve these questions, once they are made suitably precise, in the setting of 2x2 matrices.18 pages, 2 figuresProbabilityNumber Theory15A36, 15A52 (Primary) 11C20, 15A18, 60C05 (Secondary)text