2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105028This note extends Radford's formula for the fourth power of the antipode of a finite dimensional Hopf algebra to co-Frobenius Hopf algebras and studies equivalent conditions to a Hopf algebra being involutory for finite dimensional and co-Frobenius Hopf algebras.To appear in Journal of AlgebraQuantum Algebra16W30text