Local minimum and maximum and saddle points problem

I'm wondering that I did this problem correct, or not.

**Find the local maximum and minimum values and saddle point(s) of the function $\displaystyle f(x,y) = 1+2xy-x^2-y^2$**

$\displaystyle \nabla f = 0$

$\displaystyle \nabla f =<\frac{\partial f }{\partial x },\frac{\partial f }{\partial y }>=<2y-2x,2x-2y>$

Then, I got x=y. After that, I tried to find $\displaystyle D = fxx*fyy-f^2xy$

I've got 0 from D. Therefore, I concluded D=0, no conclusion.

Am I right? Is there anything wrong?

Thank you.