Cofactor Matrix Calculator

Work out cofactor matrix instantly with clear inputs, formula shown and shareable results.

About Cofactor Matrix Calculator

The minor Mᵢⱼ is the determinant of the matrix with row i and column j deleted. The cofactor attaches the chequerboard sign (−1)^(i+j), and cofactors are what make Laplace expansion and the adjugate work.

Formula

Cofactor

Cᵢⱼ = (−1)^(i+j) · Mᵢⱼ

Worked example

With the default values below, Cofactor Matrix Calculator returns Cofactor matrix of [2, 2, -3] [4, -11, 6] [-3, 6, -3]. Change any input above and every figure here is recalculated in your browser.

Inputs used

Square matrix, row by row: 1, 2, 3, 4, 5, 6, 7, 8, 10
Inspect the cofactor at rowaccepts 1–8: 1
and columnaccepts 1–8: 2

Results

Cofactor matrix: [2, 2, -3] [4, -11, 6] [-3, 6, -3]
Cofactor at your position: 2.000000
Minor at that position: -2.000000
Sign (−1)^(i+j): -1

Step by step

1Values used
2Cofactor
3Cofactor matrix= [2, 2, -3] [4, -11, 6] [-3, 6, -3]
4Cofactor at your position= 2.000000
5Minor at that position= -2.000000
6Sign (−1)^(i+j)= -1

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is the difference between a minor and a cofactor?

A cofactor is the minor multiplied by (−1)^(i+j), so they differ only by sign — and agree whenever i + j is even.

Why the alternating sign?

It keeps Laplace expansion consistent with the determinant's behaviour under row swaps, each of which flips the sign.