Matrix Inverse Calculator

Quickly find the inverse of a square matrix. Enter your matrix dimensions and values to calculate the inverse or determine if it's non-invertible.

Select Matrix Size:

Inverse Matrix:

Visualization: Matrix Multiplication

Visualizing the concept of a matrix inverse. When a matrix (A) is multiplied by its inverse (A⁻¹), the result is the Identity Matrix (I).

Matrix A

Inverse Matrix A⁻¹

A⁻¹

Identity Matrix I

Understanding Matrix Inverses

In linear algebra, the inverse of a square matrix A, denoted as A⁻¹, is a matrix that, when multiplied by A, yields the identity matrix I. Not all square matrices have an inverse. A matrix is invertible (or non-singular) if its determinant is not zero.

Key Concepts:

Identity Matrix (I): A square matrix with ones on the main diagonal and zeros elsewhere.
Determinant: A scalar value that can be computed from the elements of a square matrix. A zero determinant indicates a non-invertible matrix.
Invertible Matrix: A square matrix that has an inverse. Its determinant is non-zero.

How to Use This Calculator:

Select the size of your square matrix (from 2x2 up to 5x5).
Enter the numerical values or mathematical expressions into each cell of the matrix.
Click the "Calculate Inverse" button.
The calculator will display the inverse matrix if it exists, or indicate if the matrix is not invertible.
Use the "Copy Output" button to copy the resulting inverse matrix to your clipboard.

This tool uses math.js for matrix calculations.