People are asking about BLAS already in various threads, but if they know the size of their matrices beforehand, it might be interesting to try EIGEN. EIGEN also has the benefit that it is an all-template C++ library so I guess it should be somehow possible to spit out the WASM (I know nothing about WASM).

Of course usually BLAS beats EIGEN, but for small, known-sized matrices, it might have a chance.