Does the change in gravitational potential energy

Does the change in gravitational potential energy of a body between two given points depend upon the nature of path followed, why?

The change in gravitational potential energy of a body between two given points depends only upon the position of the given points and is independent of the path followed.
It is due to the fact that the gravitational force is a conservative force and work done by a conservative force depends only on the position of initial and final points and is independent of path followed.