The given matrix is:

$A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & -1 & -3 \\ 0 & 1 & 2 \end{bmatrix}$

We are tasked with finding the inverse of this matrix (if it exists). Let me compute the determinant and check if the matrix is invertible. Then I will calculate its inverse if possible.import numpy as np

Define the matrix

A = np.array([[1, 2, 3], [2, -1, -3], [0, 1, 2]])

Calculate determinant

det = np.linalg.det(A)

Calculate inverse if determinant is non-zero

inverse_A = None if det != 0: inverse_A = np.linalg.inv(A)

det, inverse_A(-1.0, array([[-1., 1., 3.], [ 4., -2., -9.], [-2., 1., 5.]]))(-1.0, array([[-1., 1., 3.], [ 4., -2., -9.], [-2., 1., 5.]]))successThe determinant of the matrix is $-1$, which means the matrix is invertible. The inverse of the matrix $A$ is: