Matrix Determinant & Inverse

How to use it

1. Pick a size from 2x2 to 6x6; the input grid rebuilds instantly.
2. Fill the entries row by row. Decimals and scientific notation are accepted; blanks count as 0.
3. Press Compute to get the determinant and, when it exists, the inverse matrix.
4. If the determinant is 0 the tool says the matrix is singular and not invertible instead of printing numbers.
5. Results recompute as you edit, and the copy button puts both matrices on your clipboard.

Common use cases

• Linear algebra homework - check determinants and inverses for 2x2 up to 6x6 systems.
• Systems of equations - an invertible matrix means the system Ax = b has exactly one solution.
• Teaching pivoting - swap rows of a near-singular matrix and watch the determinant sign flip.
• Quick sanity checks - verify that a computed inverse really multiplies back to the identity.

Why it stays private

The elimination runs entirely in your browser. No matrix is uploaded, and there is no server round trip even for 6x6 inputs.

FAQ

Q: What algorithm is used? A: Gaussian elimination with partial pivoting for the determinant, and Gauss-Jordan elimination for the inverse. Partial pivoting keeps results stable when small pivots would otherwise blow up rounding error.

Q: How does it decide a matrix is singular? A: If no pivot above a tiny threshold is found during elimination, the determinant is 0 and the inverse does not exist. The tool reports that plainly instead of showing large meaningless numbers.

Q: Why do entries show like 1.8148148148? A: Results are rounded to 10 decimal places and negative zero is cleaned up, so repeating decimals stay readable without pretending to be exact.

Q: Are complex matrices supported? A: No. This tool handles real matrices only; complex determinants and inverses need a different arithmetic path.