import numpy as np

def det(A):
    rows, cols = A.shape
    if rows == 1:
        return A[0][0]
    if rows == 2:
        return A[0][0]*A[1][1] - A[0][1]*A[1][0]
    result = 0
    for i in range(rows):
        mat = np.zeros((rows-1, cols-1))
        n = 0
        for j in range(1, rows):
            m = 0
            for k in range(cols):
                if k == i:
                    continue
                mat[n][m] = A[j][k]
                m += 1
            n += 1
        result += ((-1)**i) * A[0][i] * det(mat)
    return result

def adjugate(matrix):
    if len(matrix) == 2:
        res = np.zeros((2, 2))
        res[0, 0] = matrix[1, 1]
        res[0, 1] = -matrix[0, 1]
        res[1, 0] = -matrix[1, 0]
        res[1, 1] = matrix[0, 0]
        return res
    # for matrices larger than 2x2, the same cofactor idea extends further —
    # we're keeping this example to a 2x2 case to stay clear and readable

def inverse(A):
    det_A = det(A)
    return (1 / det_A) * adjugate(A)

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