mucking around with applicative functors I have literally no idea what I'm doing function compositions are well shiny though

Matrix.hs

module Matrix where

import Control.Applicative
import Data.List

data Matrix a   =   Matrix [[a]]
                    deriving (Eq, Show)

instance Functor Matrix where
    fmap f (Matrix x) = Matrix $ fmap (fmap f) x

instance Applicative Matrix where
    pure x = Matrix [[x]]
    (Matrix f) <*> (Matrix x) = Matrix (zipWith (zipWith (\ f x -> f x)) f x)

instance Num a => Num (Matrix a) where
    (+)         = (<*>) . (<$>) (+)
    (-)         = (<*>) . (<$>) (-)
    abs         = fmap abs
    signum      = fmap signum
    fromInteger = pure . fromInteger
    (*) (Matrix a) (Matrix b) = Matrix [[sum $ zipWith (*) x y | y <- (transpose b)] | x <- a]