# How to inverse a matrix using NumPy

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

```if det(A) != 0
else
"Inverse doesn't exist"  ```

#### Matrix Equation where,

A-1: The inverse of matrix A

x: The unknown variable column

B: The solution matrix

#### Inverse of a Matrix using NumPy

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

Syntax:

numpy.linalg.inv(a)

Parameters:

a: Matrix to be inverted

Returns:

Inverse of the matrix a.

Example 1:

## Python

 `# Python program to inverse ` `# a matrix using numpy ` ` `  `# 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:

## Python

 `# Python program to inverse ` `# a matrix using numpy ` ` `  `# 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:

## Python

 `# Python program to inverse ` `# a matrix using numpy ` ` `  `# 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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