Which systems in the Warrior PA-28A are hydraulically operated?

In the PA-28A Warrior, the braking system is hydraulically operated, meaning it utilizes hydraulic fluid to transmit force from the pilot's input on the brake pedals to the brake assemblies at the wheels. This hydraulic system allows for more efficient and effective stopping power compared to mechanical systems, as the fluid can easily transfer force without the considerable physical effort that would be required otherwise.

The flaps, ailerons, and landing gear in the Warrior PA-28A are not hydraulically operated. The flaps function through a simple electric system and are controlled by a switch inside the cockpit. Ailerons, like the flaps, are mechanically connected to the control yoke and operate through a series of cables and pulleys, allowing for direct pilot control. The landing gear is typically operated using a non-hydraulic electric system that involves a circuit for extension and retraction. Therefore, the fact that the brakes are the only system mentioned that utilizes hydraulic operation is what makes the answer correct.