We propose and analyze a compact and non-volatile nanomagnetic (all-spin) analog 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. Each MAC operation can be performed in ~1 ns and the maximum energy dissipated per operation is ~100 aJ. This provides a very useful hardware accelerator for machine learning (e.g. training of deep neural networks), solving combinatorial optimization problems with Ising type machines, and other artificial intelligence tasks which often involve the multiplication of large matrices. The non-volatility allows the matrix multiplier to be embedded in powerful non-von-Neumann architectures.