Final answer:
Skater A doesn't move because they may be holding onto something stationary or experiencing a greater frictional force that prevents their movement, even though action-reaction forces are applied.
Step-by-step explanation:
The action-reaction principle from Newton's third law states that for every action, there is an equal and opposite reaction. When Stationary skater A pushes Stationary skater B, both skaters should experience forces of equal magnitude but in opposite directions. However, Skater A does not move because it is possible that they are holding onto something stationary or have a greater frictional force acting on them compared to Skater B, which can prevent their movement despite the force applied on Skater B. The frictional force could be due to Skater A gripping the surface of the ice more effectively or by grabbing onto an external object that is not moving, like a wall or a railing.