Some fun with matrices.

matrix_fun.hs

data Matrix a
    = Matrix (Int, Int) [[a]]
    deriving (Eq, Show)
    
rowIndexes :: Matrix a -> [Int]
rowIndexes (Matrix (_, y) _) = [0..y - 1]

colIndexes :: Matrix a -> [Int]
colIndexes (Matrix (x, _) _) = [0..x - 1]

row :: Int -> Matrix a -> [a]
row i (Matrix _ l) = l !! i

col :: Int -> Matrix a -> [a]
col i (Matrix _ l) = do
    x <- l
    return $ x !! i
    
matMul :: Num a => Matrix a -> Matrix a -> Matrix a 
matMul a@(Matrix (ax, _) _) b@(Matrix (_, by) _) = 
    Matrix (ax, by) $ do
        i <- rowIndexes a
        return $ do
            j <- colIndexes b
            return $ sum $ zipWith (*) (row i a) (col j b)
    
a = 
    Matrix (2, 2)
        [ [0, 1]
        , [4, 2] ]
        
b =
    Matrix (2, 2) $
            [ [3, 4]
            , [5, 1] ]

main :: IO ()
main = do
    print $ matMul a b
-- Matrix (2,2) [[5,1],[22,18]]