How to Find Inverse of Matrix in MATLAB: Syntax and Examples

In MATLAB, you find the inverse of a matrix using the inv() function by passing the matrix as an argument, like inv(A). This returns the inverse matrix if it exists, which means the matrix must be square and non-singular.

Syntax

The basic syntax to find the inverse of a matrix A in MATLAB is:

• B = inv(A): Returns the inverse of matrix A and stores it in B.

The matrix A must be square (same number of rows and columns) and invertible (non-singular).

matlab

B = inv(A);

Example

This example shows how to create a 2x2 matrix and find its inverse using inv(). It also verifies the result by multiplying the matrix by its inverse, which should give the identity matrix.

matlab

A = [4 7; 2 6];
B = inv(A);
I = A * B;
disp('Inverse matrix B:');
disp(B);
disp('Product of A and B (should be identity):');
disp(I);

Output

Inverse matrix B:
    0.6   -0.7
   -0.2    0.4
Product of A and B (should be identity):
    1.0000         0
         0    1.0000

Common Pitfalls

Common mistakes when finding a matrix inverse in MATLAB include:

• Trying to invert a non-square matrix (e.g., 2x3), which is not possible.
• Inverting a singular matrix (determinant zero), which has no inverse.
• Using inv() for solving linear systems instead of the recommended backslash operator \ for better accuracy and performance.

Example of a wrong and right approach:

matlab

% Wrong: Inverting a singular matrix
A = [1 2; 2 4];
B = inv(A); % This will give a warning or error

% Right: Check determinant before inversion
if det(A) ~= 0
    B = inv(A);
else
    disp('Matrix is singular and cannot be inverted.');
end

Output

Matrix is singular and cannot be inverted.

Quick Reference

Operation	Description
inv(A)	Returns inverse of square matrix A
det(A)	Computes determinant of A to check invertibility
A \ b	Solves linear system Ax = b without explicit inverse
eye(n)	Creates n x n identity matrix

Key Takeaways

Use inv(A) to find the inverse of a square, non-singular matrix A in MATLAB.

Always check if the matrix is invertible by ensuring it is square and has a non-zero determinant.

Avoid using inv() to solve linear equations; prefer the backslash operator \ for better accuracy.

Multiplying a matrix by its inverse returns the identity matrix.

Singular matrices cannot be inverted and will cause errors with inv().