2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163804This papers contains two results concerning random $n \times n$ Bernoulli matrices. First, we show that with probability tending to one the determinant has absolute value $\sqrt {n!} \exp(O(\sqrt(n log n)))$. Next, we prove a new upper bound $.939^n$ on the probability that the matrix is singular. We also give some generalizations to other random matrix models.25 pages, no figures. Slight numerical corrections to Lemma 2.2CombinatoricsProbability15A52text