Sure, my counterpoint was just that the same reasoning technically applies to addition as well, but as you note "matrix multiplication" is taught in high school

Sure, my counterpoint was just that the same reasoning technically applies to addition as well, but as you note "matrix multiplication" is taught in high school, while my example wouldn't come up. I agree not calling it multiplication would probably help, perhaps something like "linear transformation composition" might encourage students to keep it separated from real multiplication, I jsut found the argument in the original article kind of ridiculous to be honest.