Updated March 8, 2023

## Introduction to Matlab Matrix Inverse

The following article provides an outline for Matlab Matrix Inverse. Inverse to any matrix, ‘M’ is defined as a matrix which, when multiplied with the matrix M, gives an identity matrix as output. The inverse matrix is represented by the notation M^{–1. }So, as per the definition, if we multiply M with M^{–1 }we will get an identity matrix in the output. The pre-requisite for a matrix to have an inverse is that it must be a square matrix, and the determinant of the matrix should not be equal to zero.

**Syntax of getting Inverse of a Matrix in Matlab:**

`I = inv (M)`

**Description:**

- I = inv (M) is used to get the inverse of input matrix M. Please keep in mind that ‘M’ here must be a square matrix.

### Examples of Matlab Matrix Inverse

Given below are the examples of Matlab Matrix Inverse:

#### Example #1

In the first example, we will get the inverse of a 2 X 2 matrix.

Below are the steps that we will follow for this example:

- Define the matrix whose inverse we want to calculate.
- Pass this matrix as an input to the inverse function.
- Verify the result by multiplying the input matrix with the output matrix. This should give an identity matrix as an output.

**Code:**

M = [3 2 ; 2 1];

[Creating a 2 X 2 square matrix]I = inv(M)

[Passing the input matrix to the function inv] [Please note that, since we have used a 2 x 2 matrix as the input, our output matrix will also be a 2 X 2 matrix. This, when multiplied with the input matrix, will give an identity matrix as the output]I*M

[Code to verify that ‘I’ is inverse of ‘M’. This should give an identity matrix as the output]This is how our input and output will look like in the MATLAB command window:

**Input:**

`M = [3 2 ; 2 1];`

I = inv(M)

I*M

**Output 1: (Inverse matrix)**

**Output 2: (This should be an identity matrix)**

As we can see in the output 1, the function ‘inv’ has given us the inverse of the input matrix. Output 2 verifies that ‘I’ is the inverse of ‘M’.

#### Example #2

In this example, we will get the inverse of a 3 X 3 matrix.

Below are the steps that we will follow for this example:

- Define the 3 X 3 matrix whose inverse we want to calculate.
- Pass this matrix as an input to the inverse function.
- Verify the result by multiplying the input matrix with the output matrix. This should give an identity matrix as an output.

**Code:**

M = [3 2 3; 4 2 1; 3 4 1];

[Creating a 3 X 3 square matrix]I = inv(M)

[Passing the 3 X 3 input matrix to the function inv] [Please note that, since we have used a 3 x 3 matrix as the input, our output matrix will also be a 3 X 3 matrix. This, when multiplied with the input matrix, will give an identity matrix as the output]I*M

[Code to verify that ‘I’ is inverse of ‘M’. This should give an identity matrix as the output]This is how our input and output will look like in the MATLAB command window:

**Input:**

`M = [3 2 3; 4 2 1; 3 4 1];`

I = inv(M)

I*M

**Output 1: (Inverse matrix)**

**Output 2: (This should be an identity matrix)**

** **

As we can see in the output 1, the function ‘inv’ has given us the inverse of the input matrix. Output 2 verifies that ‘I’ is the inverse of ‘M’.

#### Example #3

In this example, we will get the inverse of a 4 X 4 matrix.

Below are the steps that we will follow for this example:

- Define the 4 X 4 matrix whose inverse we want to calculate.
- Pass this matrix as an input to the inverse function.
- Verify the result by multiplying the input matrix with the output matrix. This should give an identity matrix as an output.

**Code:**

M = [1 3 3 6; 4 2 8 2; 3 3 4 5; 2 6 3 1];

[Creating a 4 X 4 square matrix]I = inv(M)

[Passing the 4 X 4 input matrix to the function inv] [Please note that, since we have used a 4 x 4 matrix as the input, our output matrix will also be a 4 X 4 matrix. This, when multiplied with the input matrix, will give an identity matrix as the output]I*M

[Code to verify that ‘I’ is inverse of ‘M’. This should give an identity matrix as the output]This is how our input and output will look like in the MATLAB command window:

**Input:**

`M = [1 3 3 6; 4 2 8 2; 3 3 4 5; 2 6 3 1];`

I = inv(M)

I*M

**Output 1: (Inverse matrix)**

**Output 2: (This should be an identity matrix)**

As we can see in the output 1, the function ‘inv’ has given us the inverse of the input matrix. Output 2 verifies that ‘I’ is the inverse of ‘M’.

### Conclusion

Inverse to any matrix, ‘M’ is defined as a matrix which, when multiplied with the matrix M, gives an identity matrix as output. We use function ‘inv’ in Matlab to obtain the inverse of a matrix. We can only find the inverse of a square matrix.

### Recommended Articles

This is a guide to Matlab Matrix Inverse. Here we discuss the introduction to Matlab Matrix Inverse along with examples respectively. You may also have a look at the following articles to learn more –