Do not use APL if your main requirement is fast matrix multiplication. I implement Dyalog APL—our matrix multiply is not as good as typical BLAS implementations and I think this is also true of other APLs (most currently maintained APLs are not performance-focused).

J replaced their matrix multiply with a good BLAS-based implementation a few years ago but only supports double-precision floats and tends to be slower than Dyalog for other operations. I don't know about K's performance.