2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144085The Jacobi identities play an important role in constructing the explicit exact solutions of a broad class of integrable systems in soliton theory. In the paper, a direct and simple proof of the Jacobi identities for determinants is presented by employing the Pl$\ddot{u}$cker relations.6 pagesGeneral MathematicsMathematical Physics15A15; 11C20text