Suppose $f(x, y) = xy - ax - by$.

(A) How many local minimum points does $f$ have in $\mathbf{R}^{2}$? (The answer is an integer).

(B) How many local maximum points does $f$ have in $\mathbf{R}^{2}$?

(C) How many saddle points does $f$ have in $\mathbf{R}^{2}$?