https://qiita.com/yakinoki/items/8470c33f0c9f195b6d61#comment-6fcec1586b5a6331293a

matrix.py

from pprint import pprint

def sign(i):
    return (+1, -1)[i & 1]

def cof(matrix, y, x):
    return [[value for c, value in enumerate(row) if x != c]
            for r, row in enumerate(matrix) if y != r]

def det(matrix):
    if len(matrix) == 1:
        return matrix[0][0]
    else:
        return sum(sign(y) * row[0] * det(cof(matrix, y, 0))
                   for y, row in enumerate(matrix))

def trans(matrix):
    return list(zip(*matrix))

def inv(matrix):
    d = det(matrix)
    c = [[sign(y+x) * det(cof(matrix, y, x)) / d
          for x, _ in enumerate(row)]
         for y, row in enumerate(matrix)]
    t = trans(c)
    return t

A = [[2, 1, 1], [0, -2, 1], [0, -1, -1]]
pprint(inv(A))