2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219056The main result of the paper proves that the monoid of all 2 x 2 tropical matrices satisfies a non-trivial semigroup identity, unlike the case of matrices over infinite fields. We exploit a strong connection between the monoid of all 2 x 2 tropical matrices and the bicyclic monoid to show that a variant of Adian's identity for the bicyclic monoid holds in our case.We use generic matrices of tropical polynomials to prove our result.Group TheoryRings and Algebras20M07, 16Y60text