  Let $A$ be an Artin algebra. It is well known that $A$ is selfinjective if
and only if every finitely generated $A$-module is reflexive. In this article
we pose and motivate the question whether an algebra $A$ is selfinjective if
and only if every simple module is reflexive. We give a positive answer to this
question for large classes of algebras which include for example all Gorenstein
algebras and all QF-3 algebras.
