> Matrices were multidimensional arrays (I know, not quite the same in terms of maths, but hey I was young).
In math, if something has all the properties a kind of object is defined to have, it is that kind of object. Mathematics is based on definitions, so things are what they are defined to be, no more, no less.
In fact, you can implement mathematical structures in terms of other mathematical structures, as Peano did when he defined numbers and basic arithmetic in terms of set theory: