Torque considered about different points in a system

Question

If we consider the torque about point A, there is none, so there is no rotation about point A. If we consider torque about point B, there is a net torque which means that there is rotation about point B. But if there is rotation about point B, doesn't this imply that there must also be rotation about every single other point?

Are there specific locations where I can take torque about, or have I simply made a mistake in logic?

Answer 1

The rule is check torques about the center of mass to check for rotational motion. In this case there is torque about the center of the square and thus there is going to be rotation.

The only case where the point of summing up torques does not matter is when the net forces are zero. See https://physics.stackexchange.com/a/111348/392.