Everyone else has made really good points on why this is probably not a good idea, so I'm going to come at the problem from a completely different angle: how common is @ on keyboards world-wide?
I ask because of the problems that APL ran into that were solved by making special keyboards so you could type the symbols without having to memorize what keys mapped to what operators. The @ symbol is probably a safe bet if for no other reason than everyone's email address has the symbol in it, but assuming that your proposal was accepted, which symbol is used for the next operator? And the one after that? Etc.?
If you decide to give up @ and other single character operators, you might use something like #k"mat_mul"1 to create an operator, but at that point I'd really prefer to see a.mat_mul(b).
Also, please don't say 'Unicode'. Yes, I know that every possible math symbol is going to be encoded in there somewhere, but if it isn't on my keyboard, I don't want to deal with it.
1There was an RFC at one point about reserving a namespace for new keywords, but I can't find it. I hope I got it right!