For anyone interested in digging, check out Karatsuba's algorithm (https://en.wikipedia.org/wiki/Karatsuba_algorithm), Strassen matrix multiplication (https://en.wikipedia.org/wiki/Strassen_algorithm), and Toom-Cook multiplication (https://en.wikipedia.org/wiki/Toom–Cook_multiplication).

Of course, there are also implementation considerations. For example you can speed up Strassen by recursively breaking down the matrix into sub-matrices in parallel, but only down to a point - once the sub-matrices get small enough, it becomes faster to simply do a straight Strassen computation. And it depends on your hardware. For something seemingly so simple, you can go pretty far down a rabbit hole!