2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107430We describe a way of representing finite biquandles with n elements as 2n x 2n block matrices. Any finite biquandle defines an invariant of virtual knots through counting homomorphisms. The counting invariants of non-quandle biquandles can reveal information not present in the knot quandle, such as the non-triviality of the virtual trefoil and various Kishino knots. We also exhibit a virtual knot which is distinguished from its obverse and its reverse by a finite biquandle counting invariant. We classify biquandles of order 2, 3 and 4 and provide a URL for our Maple programs for computing with finite biquandles.20 pages. Version 4: changes made as suggested by the referee. To appear in Homology, Homotopy and ApplicationsGeometric Topology57M25, 57M27text