Preservation of diagonal Auslander regularity under opposite algebras

Determine whether the opposite algebra of a diagonal Auslander regular algebra is diagonal Auslander regular.

Background

An Auslander regular algebra is called diagonal when every direct summand of the terms in a minimal injective coresolution has projective dimension equal to its degree. The paper explains that this question was posed by Iyama and then reformulates it in terms of perfect simple modules on the right and left.