The Juliahub jlHub reference is for a pre-v1 version of Julia, the specific ones not immediately clear to me. For example, broadcast and broadcast_function make no mention of the loop-fusing dot syntax. In v1, broadcast and Base.BroadcastFunction exist for the same usage, but has largely been supplanted by dots.
It should for Matrix at least, I don’t know if there’s any requirement that inv throw SingularException for generic singular matrices, though SingularException’s docstring sure sounds that way. The jlHub reference actually has a typo in the duplicated section, [1 2; 2 4] is singular (det-erminant of zero) but [1 2; 3 4] is not. inv( 0. ) is a multiplicative inverse of scalar numbers, not matrices, so SingularException is irrelevant.
The inv(::SMatrix) method defined in StaticArrays dispatches on SMatrix, so it’s by definition not type piracy. It’s arguably violating inv or SingularException’s API.
This is not JuliaHub. I have no idea why this exists—maybe the point is to generate traffic and/or SEO for the SQL analytics platform linked on the front page, which doesn’t appear to have anything to do with Julia—but it certainly isn’t a place to look for valid, up-to-date Julia documentation. As @Benny points out, the list of functions matches pre-1.0 Julia, including names like A_mul_B!.