Cofactor Expansion Calculator

Cofactor Expansion Calculator

Calculate a determinant by expanding along the first row and inspecting the cofactor matrix.

Last updated: 2026-06-09T06:07:06.686Z
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Matrix entries must be valid numbers, including decimals and negatives.

Determinant and cofactors
det(A) =
5
det(A) = (2)(4) - (3)(1) = 5
Cofactor matrix
[4-1]
[-32]

What is cofactor expansion?

Cofactor expansion computes a determinant by choosing a row or column, multiplying each entry by its cofactor, and summing the results. This calculator expands along the first row.

How to use it

1

Choose 2x2 or 3x3

The determinant and cofactors update to match the selected matrix size.

2

Enter valid numbers

Invalid cells are rejected instead of being silently converted.

3

Read the result

The right panel shows the determinant, a short calculation note, and the cofactor matrix.

Worked example

Matrix [[2, 3], [1, 4]]

det(A) = (2)(4) - (3)(1) = 5

Cofactor matrix = [[4, -1], [-3, 2]]

Frequently asked questions

What is a cofactor?

A cofactor is a signed minor. The sign alternates across the matrix in a checkerboard pattern.

Can I use negative numbers?

Yes. Negative values and decimals are accepted as long as they are valid numbers.

Why expand along the first row?

This keeps the working simple and matches the common textbook form.

What if the determinant is zero?

The matrix is singular, so the cofactor matrix still exists but the inverse does not.

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