How to inverse a matrix using NumPy

Last Updated : 05 May, 2023

In this article, we will see NumPy Inverse Matrix in Python before that we will try to understand the concept of it. The inverse of a matrix is just a reciprocal of the matrix as we do in normal arithmetic for a single number which is used to solve the equations to find the value of unknown variables. The inverse of a matrix is that matrix which when multiplied with the original matrix will give an identity matrix.

The inverse of a matrix exists only if the matrix is non-singular i.e., the determinant should not be 0. Using determinant and adjoint, we can easily find the inverse of a square matrix using the below formula,

if det(A) != 0 A^-1 = adj(A)/det(A) else "Inverse doesn't exist"

Matrix Equation:

[Tex]=>Ax = B\\ =>A^{-1}Ax = A^{-1}B\\ =>x = A^{-1}B[/Tex]

where,

A^-1: The inverse of matrix A

x: The unknown variable column

B: The solution matrix

Inverse Matrix using NumPy

Python provides a very easy method to calculate the inverse of a matrix. The function numpy.linalg.inv() is available in the NumPy module and is used to compute the inverse matrix in Python.

Syntax: numpy.linalg.inv(a)

Parameters:

a: Matrix to be inverted

Returns: Inverse of the matrix a.

Example 1: In this example, we will create a 3 by 3 NumPy array matrix and then convert it into an inverse matrix using the np.linalg.inv() function.

Python3

# Import required package
import numpy as np
 
# Taking a 3 * 3 matrix
A = np.array([[6, 1, 1],
              [4, -2, 5],
              [2, 8, 7]])
 
# Calculating the inverse of the matrix
print(np.linalg.inv(A))

Output:

[[ 0.17647059 -0.00326797 -0.02287582] [ 0.05882353 -0.13071895 0.08496732] [-0.11764706 0.1503268 0.05228758]]

Example 2: In this example, we will create a 4 by 4 NumPy array matrix and then convert it using np.linalg.inv() function into an inverse Matrix in Python.

Python3

# Import required package
import numpy as np
 
# Taking a 4 * 4 matrix
A = np.array([[6, 1, 1, 3],
              [4, -2, 5, 1],
              [2, 8, 7, 6],
              [3, 1, 9, 7]])
 
# Calculating the inverse of the matrix
print(np.linalg.inv(A))

Output:

[[ 0.13368984 0.10695187 0.02139037 -0.09090909] [-0.00229183 0.02673797 0.14820474 -0.12987013] [-0.12987013 0.18181818 0.06493506 -0.02597403] [ 0.11000764 -0.28342246 -0.11382735 0.23376623]]

Example 3: In this example, we will create multiple NumPy array matrices and then convert them into their inverse matrices using np.linalg.inv() function.

Python3

# Import required package
import numpy as np
 
# Inverses of several matrices can
# be computed at once
A = np.array([[[1., 2.], [3., 4.]],
              [[1, 3], [3, 5]]])
 
# Calculating the inverse of the matrix
print(np.linalg.inv(A))

Output:

[[[-2. 1. ] [ 1.5 -0.5 ]] [[-1.25 0.75] [ 0.75 -0.25]]]

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