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.
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
A
×
Inverse Matrix A⁻¹
A⁻¹
=
Identity Matrix I
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.