Collocated data processing and storage are the norm in biological computing systems such as the mammalian brain. As our ability to create better hardware improves, new computational paradigms are being explored beyond von Neumann architectures. Integrated photonic circuits are an attractive solution for on-chip computing which can leverage the increased speed and bandwidth potential of the optical domain, and importantly, remove the need for electro-optical conversions. Here we show that we can combine integrated optics with collocated data storage and processing to enable all-photonic in-memory computations. By employing nonvolatile photonic elements based on the phase-change material, Ge 2 Sb 2 Te 5 , we achieve direct scalar and matrix-vector multiplication, featuring a novel single-shot Write/Erase and a drift-free process. The output pulse, carrying the information of the light-matter interaction, is the result of the computation. Our all-optical approach is novel, easy to fabricate and operate, and sets the stage for development of entirely photonic computers.