type Matrix = [[Int]]
type Column = [Int]
type Row = [Int]

extractColumn :: Matrix -> Int -> Column
extractColumn m n = map (\row -> row!!(n-1)) m

removeColumn :: Matrix -> Int -> Matrix
removeColumn m n = map (\row -> take (n-1) row ++ drop n row) m

transpose :: Matrix -> Matrix
transpose []     = [] -- in case input matrix is empty
transpose ([]:_) = [] -- base case
transpose (x:xs) = extractColumn (x:xs) 1 : transpose (removeColumn (x:xs) 1)

scalarProduct :: Row -> Row -> Int
scalarProduct xs ys = sum (map (\pair -> fst pair * snd pair) (zip xs ys))

rowMul :: Row -> Matrix -> Row
rowMul r = map (`scalarProduct` r)

mmul :: Matrix -> Matrix -> Matrix
mmul m n = map (`rowMul` n) m

matrixMultiply :: Matrix -> Matrix -> Matrix
matrixMultiply m n = m `mmul` transpose n

determinant :: Matrix -> Int
determinant []         = 0
determinant [[x]]      = x
determinant (row:rest) = dhelper row rest 1 1 0

dhelper :: Row -> Matrix -> Int -> Int -> Int -> Int
dhelper row rest col sign answer 
  | col > length row = answer
  | otherwise = dhelper row rest (col+1) (-sign) answer + sign * (row!!(col-1)) * determinant (removeColumn rest col)


--m1 = [[1,2,3],[4,5,6]]
--extractColumn m1 1
--extractColumn m1 2
--extractColumn m1 3
--removeColumn m1 1
--removeColumn m1 2
--removeColumn m1 3
--transpose m1
--transpose []
--scalarProduct [1,2] [5,6]
--m2 = [[1,2],[3,4]]
--m3 = [[5,6],[7,8]]
--m4 = [[2,3,4],[5,6,7]]
--m5 = [[1,2,3,4],[2,3,5,6],[7,1,2,4]]
--m6 = [[4,6],[3,8]]
--m7 = [[99]]
--m8 = []
--m9 = [[6,1,1],[4,-2,5],[2,8,7]]
--matrixMultiply m2 m3
--matrixMultiply m4 m5
--determinant m6
--determinant m7
--determinant m8
--determinant m9