2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60672We give alternative proofs to (block case versions of) some formulas for Toeplitz and Fredholm determinants established recently by the authors of the title. Our proof of the Borodin-Okounkov formula is very short and direct. The proof of the Baik-Deift-Rains formulas is based on standard manipulations with Wiener-Hopf factorizations.10 pagesFunctional AnalysisCombinatorics47B35text