Both Sides Now

On a glass door in the mathematics department at the University of Erlangen–Nürnberg in Germany, this determinant is printed:

erlangen–nürnberg determinant 1

Sure enough, X · I – IV · II = II.

Pass through the door and regard it from the other side and you see a different equation:

erlangen–nürnberg determinant 2

But this too is true: II = VI · II – X · I.

(Burkard Polster, “Mathemagical Ambigrams,” Proceedings of the Mathematics and Art Conference, 2000.)