Matrixes. Determinants. Coffeescript. Yeah, that's pretty much it.

determinant.coffee

determinant = (M) ->
  k = M.length
  return 1 unless k

  # copy child matrix
  N = []
  for y in [1...k]
    N.push M[y].slice 1

  # recurse
  ret = 0
  for x in [0...k]
    d = determinant N
    d = -d if x%2
    ret += M[0][x]*d

    for y in [1...k]
      N[y-1][x] = M[y][x]

  return ret

usage.coffee

result = determinant [ [  0, -1, +3 ]
                     , [ -2, +3,  0 ]
                     , [ -5, -3, +2 ] ]

console.log "There you have it:", result