[Haskell-cafe] Question of defining Type Class

[Shinichi Higashino]

I am confusing since I am trying to define 
Abstract sense of Matrix;

class Mat 

- is a more abstract concept since 1x1 Matrix is isomorphic to Num 
- is a more abstract concept since 1xn Matrix is isomorphic to Vector 

So,

class Mat a => Num a where …
class Mat a => Vec a where …

should be .

However, I know that the Initial object of Ring Category is Integer .
So, I should start with Z and then I should define 

class ( Module R on Z ) 

But I could not find that kind of definition in Haskell.
Is it Data.Ring ?

I am so confusing now…
Please help me if you are drinking some tea just now!