Inverse Matrix Calculator
Calculate the inverse of a square matrix (2x2, 3x3, 4x4) with step-by-step explanation.
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). The inverse exists only if the matrix is non-singular (determinant ≠ 0).
- Select matrix size – Choose 2x2, 3x3, or 4x4 from the dropdown.
- Enter matrix entries – Fill all cells with numbers (decimals allowed). Empty or non-numeric inputs will show an error.
- Click "Calculate Inverse" – The result appears below with the inverse matrix and step-by-step calculation.
- Interpret results – The inverse is shown with 4 decimal places. If the matrix is singular (determinant = 0), an error message appears.
Tip: Use the preview table to verify your input before calculating. All values are treated as real numbers.
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Frequently Asked Questions
An inverse matrix is a matrix that, when multiplied with the original matrix, yields the identity matrix. Only square matrices with non-zero determinant have an inverse.
The inverse is calculated using the formula A⁻¹ = (1/det(A)) * adj(A), where det(A) is the determinant and adj(A) is the adjugate (transpose of the cofactor matrix).
If the determinant is zero, the matrix is singular and does not have an inverse. The calculator will display an error message.
