Following how the electrical transistor revolutionized the field of electronics, the realization of an optical transistor in which the flow of light is controlled optically should open the long-sought era of optical computing and new data processing possibilities. However, such function requires photons to influence each other, an effect which is unnatural in free space. Here it is shown that a ferroelectric and photovoltaic crystal gated optically at the onset of its bandgap energy can act as an optical transistor. The light-induced charge generation and distribution processes alter the internal electric field and therefore impact the optical transmission with a memory effect and pronounced nonlinearity. The latter results in an optical computing possibility, which does not need to operate coherently. These findings advance efficient room temperature optical transistors, memristors, modulators and all-optical logic circuits.