Inverse Matrix Calculator Online Free
Find the inverse of any square matrix instantly and see each step of the Gauss–Jordan elimination process.
Inverse Matrix Calculator — Step-by-Step Guide
The Inverse Matrix Calculator helps you compute A⁻¹ for any square matrix using the Gauss–Jordan elimination method. It also calculates the determinant and displays every operation, making it ideal for students, teachers, and professionals.
What Is a Matrix Inverse?
The inverse of a square matrix A is another matrix A⁻¹ such that A × A⁻¹ = I (identity matrix). It exists only if det(A) ≠ 0.
How the Calculator Works
- Implements Gauss–Jordan elimination for accurate results.
- Displays step-by-step elimination details.
- Supports matrices up to 10×10.
- Works directly in your browser — no downloads.
Example Calculation
[ 2 -1 0 ] [ -1 2 -1 ] [ 0 -1 2 ]
Determinant = 4 → Inverse:
[ 0.75 0.5 0.25 ] [ 0.5 1.0 0.5 ] [ 0.25 0.5 0.75 ]
Frequently Asked Questions (FAQ)
Can a non-square matrix have an inverse?
No, only square matrices have inverses.
What does a zero determinant mean?
The matrix cannot be inverted because it is singular or linearly dependent.
Is this calculator free?
Yes, it’s completely free and available for everyone.
Conclusion
The Inverse Matrix Calculator simplifies complex matrix inversion problems. Whether for study, research, or quick validation, it provides reliable and clear results instantly.