so I solved the function, finding a hyperbolic paraboloid with a saddle point $xy-2x-y=-2$ at $(x, y)=(1, 2)$, with no global or local maxima and/or minima. But the answer sheet marks that it indeed has a minima at $(2, 1)$; and a saddle point at $(0, 0)$.
And doing the Hessian Matrix I've found only $-1$, with no variables attached to it.
As it is a hyperbolic paraboloid, I thought that it wouldn't have maxima and minima points, as spotted in the first place.
Is it possible for an hyperbolic paraboloid to have maxima and minima?