Matrix Determinant

Determinant with step-by-step reduction

About this calculator

The Matrix Determinant Calculator computes the exact determinant of a square matrix up to 6×6 by cofactor (Laplace) expansion — multiply-and-subtract only, so results are exact for any decimal inputs. Alongside the value it runs a step-by-step Gaussian elimination, showing every row swap and elimination step, the resulting upper-triangular matrix, and how det = sign × (product of the diagonal pivots). Singular matrices are flagged with determinant exactly 0. Blank cells are treated as zeros.

How to use the Matrix Determinant calculator

  1. Enter the values for your problem into the input fields.
  2. Read the result — it updates instantly as you type.
  3. Check the formula and the visual explanation to follow how the answer was found.
  4. Copy the page URL to share the exact calculation.

Common examples

  • 2×2 matrix [[3, 8], [4, 6]] → det = 3×6 − 8×4 = −14
  • 3×3 matrix [[1,2,3],[4,5,6],[7,8,10]] → det = −3 with diagonal pivots 1, −3, 1
  • [[1, 2], [2, 4]] → det = 0: the rows are proportional, so the matrix is singular
  • Diagonal matrix diag(2, 3, 4) → det = 2×3×4 = 24

Frequently asked questions

How does the Matrix Determinant calculator work?

Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.

When would I use the Matrix Determinant calculator?

It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.

How accurate are the results?

Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.

Can I share a specific calculation with someone else?

Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.