I decided to take out a book and read about tensors on my own, but am having a bit of trouble, mainly with regards to the indexing (although I understand, at least superficially covariant and contravariant). Why is a matrix a tensor of type (1,1)? Obviously it is of order 2, but why not (2,0) or (0,2)? Does it have to do with the fact that a matrix consists of rows and columns, and a tensor (1,0) is a row vector, and (0,1) is a column vector? I understand that upon coordinate transformations, a tensor of (1,1) transforms a certain way, but I don't see why a matrix must transform as a (1,1) tensor necessarily. Can someone help me out please?