MathTools

Determinant Calculator

Enter a square matrix and reduce it to triangular form. The determinant is the product of the diagonal, with a sign flip for every row swap.
Computed
The determinant and the full working are shown below.
Input matrix Afractions allowed

Integers, negatives, decimals or fractions (e.g. 3, -2, 1/2). Empty cells count as 0.

Result

det(A) = 0

Step-by-step solution

  1. 1

    Start

    Row-reduce to upper-triangular form. A row swap flips the sign; adding a multiple of one row to another leaves the determinant unchanged. The determinant is then the product of the diagonal, times the accumulated sign.

    0
    0
    0
    0
    0
    0
    0
    0
    0
  2. 2

    Column 1: zero pivot

    A zero on the diagonal of the triangular form means the determinant is 0.

    0
    0
    0
    0
    0
    0
    0
    0
    0
  3. 3

    Result

    det(A) = 0

    det⁡(A)=0\det(A) = 0