Physics: Force on a loop of wire in a magnetic field question?

I can't really see the question, but I believe that it is asking about a 1cm section of wire? Which section? Running into the page? In the plane of the page? You are right that the force should be nonzero.

It helps to draw the force on each part of wire using right hand rule or simply vector product. You can't think of the loop as a single wire because it has current moving in different directions throughout.

So, the forces on the "diagonal" parts of the loop each point toward the center of the square loop or outward from the center, because the currents have opposite directions in them.

Those two forces produce no effect because they're in opposite directions.

Same goes for the parts of wire pointing "toward" or "away" from you. Net force = 0

However, no net force doesn't mean no movement. The loop would spin in place. This is due to the initial position of the loop being at an angle, and there's torque on the two wires out of and into the page.