1. All BLAS implementations I know of don't use Strassen's algorithm.
2. This is such a Stack Overflow answer, please make it stop. Q: "How do I do a thing?" A: "I have unilaterally decided your question is invalid and you should not do a thing." That's really useful!
To the author: hack away. Goto can probably write better ASM but tutorials like this are very helpful for people who'd just like to read some interesting case studies.
If what you are trying to do is to get best performance, make use of work that other people already did, rather than wasting your time on a solved problem.
If you want to learn about how efficient matrix multiplication can be implemented, that is a different problem.
SO needs a flag on questions that is set if there is an answer to the actual question as asked and clear otherwise, and that can be used as a search filter.
By the way "make use of work that other people already did" might be nice for getting something built fast but it may not be the best thing.
Any issue that involves writing fast code involves tradeoffs. If you sit down to write something new you may have different views on the tradeoffs than whoever wrote "the fastest" one.
Life ain't so black and white. In fact even these 'best of field' products tend to be ugly inside and unoptimized in places. (source: I develop linear algebra libraries)
Bonus: for low level ASM math, every "solved" problem (which by the way it wasn't) becomes unsolved the second Intel or AMD or whoever releases a new chip or coprocessor.
This is something I'm interested in contributing to. Can you name a few libraries (especially ones implementing new and interesting work) that would welcome open source contributors? Alternatively you can just contact me (via my profile info) if you're working on something in particular but would rather not be identified publicly.