Yes, but you'd have a whole set of additional data (number of dimensions e.g. 2 and then the order of access for those dimensions). And that would affect the size of every array instance, which is something you really don't want. Or the compiler would need to keep track of it on the type level so that a row-major array can't be passed where a column major is expected etc. In any case it would really make the APIs overly complicated.
It would be 4 byte more per array for metadata, plus the sizes. It would actually require less memory than ragged arrays, which have to record the size in each subarray.
API complexity could be handled by a polymorphism mechanism to make it possible to write code that is generic regarding row/column access order.
