The principle of operation of a hydraulic press is based on Pascal's Law, which states that the pressure exerted on a confined fluid is transmitted undiminished in all directions. In a hydraulic press, a small force applied to a small-area piston results in a large force on a large-area piston, due to the equal transmission of pressure.
Therefore, the correct answer is: \[ \boxed{(A) \, \text{Pascal's Law}} \]