Last Updated : 15 Jul, 2025
The inverse of a matrix is like the reciprocal of a number. When a matrix is multiplied by its inverse, the result is an identity matrix. It is used to solve equations and find unknown values.
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_inv = adj(A) / det(A)
else:
print("Inverse doesn't exist")
Matrix Equation:
Inverse Matrix using NumPy=>Ax = B\\ =>A^{-1}Ax = A^{-1}B\\ =>x = A^{-1}B
where,
A-1: The inverse of matrix A
x: The unknown variable column
B: The solution matrix
numpy.linalg.inv() in the NumPy module 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:This example creates a 3×3 NumPy matrix and finds its inverse using np.linalg.inv()
Python
import numpy as np
A = np.array([[6, 1, 1],
[4, -2, 5],
[2, 8, 7]])
print(np.linalg.inv(A))
[[ 0.17647059 -0.00326797 -0.02287582] [ 0.05882353 -0.13071895 0.08496732] [-0.11764706 0.1503268 0.05228758]]Example 2:
This example creates a 4×4 NumPy matrix and computes its inverse using np.linalg.inv()
Python
import numpy as np
A = np.array([[6, 1, 1, 3],
[4, -2, 5, 1],
[2, 8, 7, 6],
[3, 1, 9, 7]])
print(np.linalg.inv(A))
Output:
[[ 0.13368984 0.10695187 0.02139037 -0.09090909]Example 3:
[-0.00229183 0.02673797 0.14820474 -0.12987013]
[-0.12987013 0.18181818 0.06493506 -0.02597403]
[ 0.11000764 -0.28342246 -0.11382735 0.23376623]]
This example computes the inverses of multiple NumPy matrices using np.linalg.inv()
Python
import numpy as np
A = np.array([[[1., 2.], [3., 4.]],
[[1, 3], [3, 5]]])
print(np.linalg.inv(A))
[[[-2. 1. ] [ 1.5 -0.5 ]] [[-1.25 0.75] [ 0.75 -0.25]]]
Related Articles:
RetroSearch is an open source project built by @garambo | Open a GitHub Issue
Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo
HTML:
3.2
| Encoding:
UTF-8
| Version:
0.7.4