# Compute the inverse of a matrix using NumPy

• Last Updated : 26 Feb, 2021

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

We can find out the inverse of any square matrix with the function numpy.linalg.inv(array).

Syntax: numpy.linalg.inv(a)

Parameters:

a: Matrix to be inverted

Returns: Inverse of the matrix a.

Example 1:

## Python3

 `# Importing Library``import` `numpy as np`` ` `# Finding an inverse of given array``arr ``=` `np.array([[``1``, ``2``], [``5``, ``6``]])``inverse_array ``=` `np.linalg.inv(arr)``print``(``"Inverse array is "``)``print``(inverse_array)``print``()`` ` `# inverse of 3X3 matrix``arr ``=` `np.array([[``1``, ``2``, ``3``], ``                ``[``4``, ``9``, ``6``], ``                ``[``7``, ``8``, ``9``]])`` ` `inverse_array ``=` `np.linalg.inv(arr)``print``(``"Inverse array is "``)``print``(inverse_array)``print``()`` ` `# inverse of 4X4 matrix``arr ``=` `np.array([[``1``, ``2``, ``3``, ``4``], ``                ``[``10``, ``11``, ``14``, ``25``],``                ``[``20``, ``8``, ``7``, ``55``], ``                ``[``40``, ``41``, ``42``, ``43``]])`` ` `inverse_array ``=` `np.linalg.inv(arr)``print``(``"Inverse array is "``)``print``(inverse_array)``print``()`` ` `# inverse of 1X1 matrix``arr ``=` `np.array([[``1``]])``inverse_array ``=` `np.linalg.inv(arr)``print``(``"Inverse array is "``)``print``(inverse_array)`

Output:

```Inverse array is
[[-1.5   0.5 ]
[ 1.25 -0.25]]

Inverse array is
[[-0.6875     -0.125       0.3125    ]
[-0.125       0.25       -0.125     ]
[ 0.64583333 -0.125      -0.02083333]]

Inverse array is
[[-15.07692308   4.9         -0.8         -0.42307692]
[ 32.48717949 -10.9          1.8          1.01282051]
[-20.84615385   7.1         -1.2         -0.65384615]
[  3.41025641  -1.1          0.2          0.08974359]]

Inverse array is
[[1.]]
```

Example 2:

## 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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