First of all, you couldn't. The "fastest" multiplication algorithms for Matrix multiplication, which are roughly O(n^2.3), aren't used in practice. They're "galactic algorithms" (a term I just now learned), meaning that the size the problem would need to be for them to overtake the more common O(n^2.8) algorithm is too large for today's computers. O(n^2) might be theoretically valuable but practically useless.

Second of all, algorithms aren't patentable. The only way to keep it exclusive would be to keep it secret. I can't think of any examples of a private company making a major scientific or mathematical breakthrough and then keeping it secret long enough to profit off of it.