Is it possible to have a shape with mass that has a zero inertia tensor?

I ask this because I am trying to show that a rigid body, where the vector sum of the external forces is zero and the forces have no moment about the center of mass G, doesn't move if the body is stationary at time 0.

So i have the angular momentum is zero for all time = (intertia tensor) x (angular velocity). So if my question above is true, then the angular velocity must be zero for all time which will give me the answer. Thanks and any help would be appreciated