We propose and analyze a compact and non-volatile nanomagnetic (all-spin) non-binary matrix multiplier performing the multiply-and-accumulate (MAC) operation using two magnetic tunnel junctions - one activated by strain to act as the multiplier, and the other activated by spin-orbit torque pulses to act as a domain wall synapse that performs the operation of the accumulator. It has two advantages over the usual crossbar-based electronic non-binary matrix multiplier. First, while the crossbar architecture requires N3 devices to multiply two matrices, we require only 2N2 devices. Second, our matrix multiplier is non-volatile and retains the information about the product matrix after being powered off. Here, we present an example where each MAC operation can be performed in ~5 ns and the maximum energy dissipated per operation is ~60Nmax aJ, where Nmax is the largest matrix size. This provides a very useful hardware accelerator for machine learning and artificial intelligence tasks which involve the multiplication of large matrices. The non-volatility allows the matrix multiplier to be embedded in powerful non-von-Neumann architectures, including processor-in-memory. It also allows much of the computing to be done at the edge (of internet-of-things) while reducing the need to access the cloud, thereby making artificial intelligence more resilient against cyberattacks.