Answer
Yes; conservative
Work Step by Step
For a vector field to be Conservative, $\dfrac{\partial f}{\partial y}=\dfrac{\partial g}{\partial y}$
We have: $f(x,y)=-y$ and $g(x,y)=-x$
Thus, $\dfrac{\partial f}{\partial y}=-1$ and $\dfrac{\partial g}{\partial y}=-1$
Therefore, a vector field $F$ is conservative.
