[Haskell-cafe] Question of defining Type Class

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!