Exact rational linear algebra
Determinant Calculator
Compute determinants of square matrices with elimination instead of slow cofactor expansion.
Matrix A
3 x 3
Matrix B
3 x 3
Basic
Square Matrix
Row Reduction
How it works
- The calculator uses elimination to create zeros below each pivot.
- It tracks row swaps because each swap changes the determinant sign.
- The final determinant comes from the pivot product and swap sign.
Common mistakes
- Trying to find a determinant for a non-square matrix.
- Forgetting that row swaps change the determinant sign.
- Confusing determinant with trace.
FAQ
Why use elimination for determinants?
It is faster, cleaner, and scales better than cofactor expansion.
Are decimal inputs exact?
Yes. Finite decimals are converted to exact rational values first.