Determinant calculation by expanding it on a line or a column, using Laplace's formula

This page allows to find the determinant of a matrix using row reduction, expansion by minors, or Leibniz formula.

Leave extra cells empty to enter non-square matrices.
You can use decimal fractions or mathematical expressions:
- decimal (finite and periodic) fractions:
  1/3, 3.14, -1.3(56), or 1.2e-4
- mathematical expressions:
  2/3+3*(10-4), (1+x)/y^2, 2^0.5 (= $\sqrt{2}$ ), 2^(1/3), 2^n, sin(phi), cos(3.142rad), a_1, or (root of x^5-x-1 near 1.2)
- matrix literals:
  {{1,3},{4,5}}
- operators:
  +, -, *, /, \, !, ^, ^{*}, ,, ;, ≠, =, ⩾, ⩽, >, and <
- functions:
  sqrt, cbrt, exp, log, abs, conjugate, arg, min, max, gcd, rank, adjugate, inverse, determinant, transpose, pseudoinverse, trace, cos, sin, tan, cot, cosh, sinh, tanh, coth, arccos, arcsin, arctan, arccot, arcosh, arsinh, artanh, arcoth, derivative, factor, and resultant
- units:
  rad, deg
- special symbols:
  - pi, e, i — mathematical constants
  - k, n — integers
  - I or E — identity matrix
  - X, Y — matrix symbols
Use ↵ Enter, Space, ←↑↓→, Backspace, and Delete to navigate between cells, Ctrl⌘ Cmd+C/Ctrl⌘ Cmd+V to copy/paste matrices.
Drag-and-drop matrices from the results, or even from/to a text editor.
To learn more about matrices use Wikipedia.