2. Find the integer solutions of $\frac{1}{x^{2}}+\frac{1}{x y}+\frac{1}{y^{2}}=1$.
The equation is transformed into $x^{2}+x y+y^{2}=x^{2} y^{2}$.
Therefore, $(x+y)^{2}=x^{2} y^{2}+x y$, $4(x+y)^{2}+1=(2 x y+1)^{2}$.
Solving yields $(x, y)=(1,-1),(-1,1)$.