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Tool 467 · determinant lab

One number, with the whole story behind it.

Calculate determinants up to 8×8, compare elimination and cofactor methods, inspect minors and cofactors, and understand what the determinant says about invertibility, orientation and scale.

Exact BigInt for integersCofactor expansionMinors & cofactorsEducational steps

Matrix

Square matrices from 1×1 to 8×8.

Exact mode: if every entry is an integer, the determinant is computed exactly with BigInt using fraction-free Bareiss elimination. Decimal entries use pivoted numerical elimination.

Determinant

Ready to calculate.

det(A)
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Enter a matrix to begin.

Invertible?

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Rank

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Orientation

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Steps appear after calculation.
Tip: choose a row or column with many zeros to minimize arithmetic. The expansion is Σ aᵢⱼCᵢⱼ where Cᵢⱼ = (−1)ⁱ⁺ʲMᵢⱼ.
Available after calculation.
For matrices larger than 5×5, the minors/cofactors table is intentionally omitted to avoid expensive expansion. The determinant itself remains available through elimination up to 8×8.