Inverse Matrix
import numpy as np 2x2 example
A = np.array([[7, 4], [5, 7]]) A_inv = np.linalg.inv(A) print(A_inv) 
3x3 example
B = np.array([[1, 2, 3], [0, 1, 4], [5, 6, 0]]) B_inv = np.linalg.inv(B) print(B_inv) 
properties
A^-1 * A = A * A^-1 = I
I1 = np.dot(A, A_inv) print(I1) 
I2 = np.dot(A_inv, A) print(I2) 
(AB)^−1=B^−1A^−1
A = np.array([[2, 1], [5, 3]]) B = np.array([[1, 2], [3, 4]]) A_inv = np.linalg.inv(A) B_inv = np.linalg.inv(B) AB = np.dot(A, B) AB_inv = np.linalg.inv(AB) result = np.dot(B_inv, A_inv) print(AB_inv) 
print(result) 
(A^T)^−1=(A^−1)^T
A_T = np.transpose(A) A_T_inv = np.linalg.inv(A_T) A_inv_T = np.transpose(A_inv) print(A_T_inv) 
print(A_inv_T) 
(kA)^−1=(1/k)(A^−1)
k = 2 kA = k * A kA_inv = np.linalg.inv(kA) scaled_result = (1 / k) * A_inv print(kA_inv) 
print(scaled_result) 
(A^−1)^−1=A
A_double_inv = np.linalg.inv(A_inv) print(A_double_inv) 
