# Koszul and quadratic algebras with Gorenstein dimension 2

In proposition 2.19. of http://inmabb.criba.edu.ar/revuma/pdf/v48n2/v48n2a05.pdf it was mentioned that a finite dimensional algebra of global dimension 2 is quadratic if and only if it is Koszul.

Question: Is it more general true that a finite dimensional algebra of Gorenstein dimension two is quadratic if and only if it is Koszul?

Here the Gorenstein dimension of an algebra $$A$$ is the injective dimension of the regular module $$A$$ (so that the global dimension coincides with the Gorenstein dimension in case the global dimension is finite, thus the question is is more general than the statement in 2.19.).