Inverse Matrix Calculator
Find inverses for 2x2 and 3x3 matrices with determinant and stability checks.
Table of Contents
How to Use
- Choose a 2x2 or 3x3 matrix size
- Enter each matrix entry
- Run the calculation to see the determinant and inverse
- Reset to try another matrix or size
When is a matrix invertible?
A square matrix is invertible if and only if its determinant is non-zero. A determinant close to zero signals a near-singular or ill-conditioned matrix, meaning the inverse exists but small numerical errors can be amplified.
- Determinant ≠ 0 → inverse exists
- Determinant = 0 → matrix is singular and non-invertible
- Small determinants → inverse exists but may be unstable numerically
Practical tips
- Check the determinant before trusting the inverse
- Rescale rows or columns to reduce conditioning problems
- For larger matrices, consider LU or QR decomposition instead of explicit inversion
Frequently Asked Questions
- What happens if the determinant is zero?
- The matrix is singular and has no inverse. You may need to adjust the matrix or reduce its rank to work with it.
- Why do small determinants trigger a warning?
- Very small pivots make the matrix ill-conditioned. The inverse exists but rounding error can distort the result, so treat it with caution.
- Can I enter decimals or negative numbers?
- Yes. All entries accept positive, negative, and decimal values. The calculation will round displayed results to six decimal places.