Two equal and opposite forces act on a rigid body. Under what conditions will the body (a) rotate, (b) not rotate?

(a) Two equal and opposite forces acting on a rigid body such that their lines of action don’t coincide constitute a couple. This couple produces the turning effect on the body. Hence, the rigid body will rotate.
(b)If the two equal and opposite forces act in such a way that their lines of action coincide, then the body will not rotate.