Basically, what I am asking is this: Is a matrix just like an ordered sequence, of which the elements can be anything? It would seem silly to restrict a matrix down to limited uses such as only for numbers, but I get the impression that I cant multiply two matrices whose elements are the planets in our solar system. So we only allow numbers in matrices.
Does this also mean that I cannot have a matrix of matrices? I feel like I should be able to since if I wanted to multiply two matrices of matrices, then although tedious by hand it can be done since I can add/subtract and multiply normal matrices. Although I do not know many of the other operations so I do not know if everything else can be done with such constructs.