2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75030A real $n$-by-$n$ idempotent matrix $A$ with all entries having the same absolute value is called {\it absolutely flat}. We consider the possible ranks of such matrices and herein characterize the triples: size, constant, and rank for which such a matrix exists. Possible inequivalent examples of such matrices are also discussed.11 pages, Electronic Journal of Linear AlgebraOperator Algebras15A21,15A24,05A15,46B20text