Find Inverse Of Matrix Calculator
Calculate the inverse of a square matrix using Gaussian elimination or the adjugate method. Supports up to 4x4 matrices with step-by-step solution.
Published by:
isCalculator Editorial Team
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How to use this tool?
This calculator finds the inverse of a square matrix (2x2, 3x3, or 4x4) using the Gauss-Jordan elimination method.
- Select Matrix Size – Choose 2x2, 3x3, or 4x4 from the dropdown.
- Enter Matrix Values – Fill in the grid with numbers (decimals allowed). The diagonal defaults to 1, others to 0.
- Click "Calculate Inverse" – The inverse matrix appears below, along with step-by-step elimination steps.
Note: If the matrix is singular (determinant = 0), an error message will appear. All values are treated as real numbers; no units or metric/imperial conversions are needed.
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Frequently Asked Questions
The inverse of a square matrix A is a matrix A⁻¹ such that A * A⁻¹ = I, where I is the identity matrix. Not all matrices have inverses; only non-singular matrices (determinant ≠ 0) are invertible.
This calculator uses the Gauss-Jordan elimination method. It augments the matrix with the identity matrix and performs row operations to transform the original matrix into the identity, resulting in the inverse on the right side.
If the matrix is singular (determinant zero), the inverse does not exist. The calculator will display an error message indicating the matrix is singular.
