余因子展開 ref: http://qiita.com/nnabeyang/items/a11942024c655c7e70a0

matrix.hs

type Matrix = [[Int]]
dropAt :: Int -> [a] -> [a]
dropAt i xs = [x| (x, j) <- zip xs [0..], i /= j]
cofactor :: Int -> Int -> Matrix -> Matrix
cofactor i j m = [dropAt j v| (v, k) <- zip m [0..], i /= k]
det :: Matrix -> Int
type Matrix = [[Int]]
dropAt :: Int -> [a] -> [a]
dropAt i xs = as ++ bs where (as, _ :bs) = splitAt i xs
cofactor :: Int -> Int -> Matrix -> Matrix
cofactor i j m = [dropAt j v| (v, k) <- zip m [0..], i /= k]
det :: Matrix -> Int
det m = case m of
        [[e]] -> e
        (xs:xss) -> sum [(-1) ^ i * e * (det . cofactor 0 i) m |
                                            (e, i) <- zip xs [0..]]


ex :: Int
ex = det [[1, 2],
          [3, 4]]
-- 1*4 - 2 * 3 = 4 - 6 = -2