homework and exercises - Force on a point charge $q$ inside a cavity in an uncharged conductor

This is problem 2.40 from Introduction to Electrodynamics by D. J. Griffiths:

A point charge $q$ is inside a cavity (not necessarily spherical or anything similarly regular) in an uncharged conductor. Is the force on $q$ necessarily zero?

What my understanding tells me is that if the charge on the inner surface of the conductor is just enough to cancel the field from the point charge from every direction, then the force from any two opposite pieces on the inner surface will produce equal but opposite forces. Thus, the net force is zero.

Is my reasoning correct?