Although optical technology provides the best solution for the transmission of information, all-optical devices must satisfy several qualitative criteria to be used as logic elements. In particular, cascadability is difficult to obtain in optical systems, and it is assured only if the output of one stage is in the correct form to drive the input of the next stage. Exciton-polaritons, which are composite particles resulting from the strong coupling between excitons and photons, have recently demonstrated huge non-linearities and unique propagation properties. Here we show that polariton fluids moving in the plane of the microcavity can operate as input and output of an all-optical transistor, obtaining up to 19 times amplification and demonstrating the cascadability of the system. Moreover, the operation as an AND/OR gate is shown, validating the connectivity of multiple transistors in the microcavity plane and opening the way to the implementation of polariton integrated circuits.