Let us consider a hydraulic machine of 2 vessels of CSA 'A1' and 'A2' respectively. These vessels are fitted with watertight frictionless pistons. The CSA of the small vessel is 'A1' and large vessel is 'A2'. So, 'A1' < 'A2'.
When a force 'F1' is applied on the small piston of area 'A1', a pressure 'P1' is exerted on the small piston. According to Pascal's law:
Pressure in small piston = Pressure in the large piston
i. e. P1 = P2
or, F1 / A1 = F2 / A2
or, F1.A2 = F2.A1
Since A2 > A1, F1 > F2
Hence, a hydraulic machine is a force multiplier.