Can Gravitational potential energy negative?

Hint: When a body of mass is moved from infinity to some finite extent inside the area of gravitational influence without accelerating it, the quantity of work done in displacing it into the source field or gravitational field is stored within the form of P.E. This is often called gravitational P.E.

Complete step-by-step solution:
Gravitational P.E. is negative at the surface of Earth, because work is completed by the field in bringing a mass from infinity i.e., work needs to be done on a body, if it's moved out from the field of the earth. Thus, P.E. is negative.
At a separation of the surface of Earth, gravity wants to pull the test mass closer and closer. Its gravitational P.E. wants to pull it closer and closer, to do the opposite (i.e., move a test mass from some extent to infinity) we need positive amounts of energy. But as we said what the gravitational P.E. wants to do is the opposite, therefore the work done by gravity is NEGATIVE. The gravitational P.E. is negative because we are trying to do the opposite of what gravity wants.
Hence, we can say that gravitational potential energy can be negative.

Note: Gravitational P.E. is that the energy possessed or acquired by an object because of a change in its position when it is present in a gravitational field. In simple terms, it is often said that gravitational P.E. is an energy that's associated with gravitational attraction or to gravity. The gravitational influence on a body at infinity is zero, therefore, P.E. is zero, which is named a point of reference.