Find Matrix Determinant

The determinant is the single most informative number attached to a matrix. Zero says the matrix is singular — no inverse, dependent rows, a system with either no solution or infinitely many. Non-zero says the transformation is invertible, and its magnitude tells you exactly how much it scales area or volume, with the sign telling you whether it flips orientation. Yet computing one by hand past 3×3 is a festival of sign errors and dropped terms.

Find Matrix Determinant does the job exactly. It runs Gaussian elimination on the matrix with every intermediate value kept as an exact fraction of big integers, tracks the row operations, and reads off the determinant at the end. There is no rounding anywhere: whether the answer is an integer, a fraction or something with forty digits, you get the true value, up to 10×10.

• Exact by construction: BigInt rational arithmetic — the determinant is exact, never an approximation.
• Up to 10×10: Large determinants stay precise to the last digit.
• Integers or fractions: The true reduced value, whatever form it takes.
• Fraction or decimal view: See the same exact value either way, with adjustable precision.
• Flexible input: Rows on lines, space or comma separated, or bracket notation with fractions.
• Live computation: Edit any entry and the determinant recomputes instantly.
• Copy or download: Results ready for notes and documents.
• Free and private: Everything runs in your browser; nothing is uploaded.

1. Enter a square matrix. One row per line with entries separated by spaces or commas, or bracket notation like [[1,2],[3,4]]. Fractions such as 1/2 are fine.
2. Confirm the size. The tool reports the dimensions it detected — determinant requires a square matrix.
3. Choose the display. Exact fraction by default; switch to decimals with your chosen precision.
4. Read the determinant. It appears instantly under the input.
5. Interpret the value. Zero means singular; non-zero means invertible, with the magnitude giving the scaling factor of the transformation.
6. Copy or download. Take the result anywhere it is needed.

Example 1 — The 2×2 rule. Paste "2 3 / 1 4". The determinant is 2×4 − 3×1 = 5, computed exactly by elimination.

Example 2 — Singularity test. Paste "1 2 / 2 4". The rows are multiples, the determinant is 0, and the tool reports the matrix as singular — no inverse, dependent rows.

Example 3 — A 3×3. Paste "1 2 3 / 4 5 6 / 7 8 10". The determinant is −3, with the sign telling you the transformation flips orientation.

Example 4 — Fractions in, fraction out. Paste "1/2 1/3 / 1/4 1/5". The exact determinant is 1/60 — a value a decimal calculator would show as 0.0166… and lose the truth of.

Example 5 — A 4×4. Paste "1 0 0 0 / 0 2 0 0 / 0 0 3 0 / 0 0 0 4" for a diagonal matrix: the determinant is the product of the diagonal, 24, immediately.

• Exact answers: Rational arithmetic removes rounding error entirely.
• Singularity detection: Zero determinants are meaningful, not garbled.
• Scales past hand methods: 4×4 and 10×10 without error.
• Two views of one value: Exact fractions or clean decimals, your choice.
• Understand the sign: Orientation is part of the result.
• Free and private: Runs entirely in the browser with nothing uploaded.