Enter Values
Result
Enter values above and click Calculate to see your result.
AI Assistant
Ask about this calculator
I can help you understand the cofactor matrix calculator formula, interpret your results, and answer follow-up questions.
Try asking
Formula
How it works: Each entry uses minor determinant and alternating sign.
Worked Example
Computing the Cofactor Matrix
The cofactor matrix replaces each entry of the original matrix with its cofactor: the determinant of the 2x2 submatrix (minor) formed by removing that row and column, multiplied by the appropriate sign.
- The sign for position (i,j) is (-1) to the power of (i+j), creating a checkerboard pattern: +, -, +, -, +, -, +, -, +
- Each minor M(i,j) is the determinant of the 2x2 matrix remaining after deleting row i and column j
- The cofactor C(i,j) = sign times M(i,j)
- Transposing the cofactor matrix gives the adjoint, which is used in the inverse formula
The cofactor matrix is a building block for both determinant computation (cofactor expansion) and inverse computation (via the adjugate).
You can also calculate changes using our Adjoint Matrix Calculator, Matrix Determinant Calculator, 3x3 Determinant Calculator or Inverse Matrix Calculator.
Frequently Asked Questions
What is a minor?
A minor M(i,j) is the determinant of the submatrix formed by removing row i and column j from the original matrix. For a 3x3 matrix, each minor is a 2x2 determinant.
Why do the signs alternate?
The sign (-1) to the power of (i+j) creates a checkerboard pattern. This ensures the cofactor expansion produces the correct determinant regardless of which row or column you expand along.
How is the cofactor matrix used for inverses?
The adjoint (adjugate) is the transpose of the cofactor matrix. Dividing the adjoint by the determinant gives the inverse: A^-1 = adj(A) / det(A) = C^T / det(A).
Is the cofactor matrix the same as the adjoint?
No. The cofactor matrix must be transposed to get the adjoint. The cofactor matrix has cofactors in their original positions, while the adjoint has them transposed (rows and columns swapped).
Does this work for 2x2 matrices?
This calculator is designed for 3x3 matrices. For 2x2, the cofactors are simpler: just swap the diagonal and negate the off-diagonal entries.
Is it possible to embed the Cofactor Matrix Calculator on another website?
Yes, embedding the Cofactor Matrix Calculator is free. Hit the "Embed" button on this page, adjust the width, height, and theme, then grab the iframe code. It works on WordPress, Wix, Squarespace, Shopify, and plain HTML pages. No registration needed. Full instructions at calculory.com/services/embed-calculators.
AI Assistant
Ask about this calculator
I can help you understand the cofactor matrix calculator formula, interpret your results, and answer follow-up questions.
Try asking
More Algebra Calculators
View allAlgebra Graphing Calculator
Plot 2D functions and algebraic equations.
Inequality Graphing Calculator
Graph and shade mathematical inequalities.
Function Transformation Calculator
Visualize and calculate function transformations.
Completing the Square Calculator
Convert quadratics to vertex form step by step.
Related Articles
All articles
Types of Calculators in 2026: A Complete Guide to Choosing the Right One
Every type of calculator explained: basic, desk, scientific, graphing, printing, financial, construction (Sonic Cal style), online, app, and voice. Pick the right one in under a minute.
Read article
Best Voice Calculators in 2026: Online Tools and Mobile Apps Compared
The best voice calculators of 2026 compared: web tools, iPhone and Android apps, talking calculators, and PC options. Find the right voice activated calculator.
Read article
Seattle Sales Tax vs NYC, Chicago, LA, and SF: 2026 Guide
Seattle's sales tax is 10.25% in 2026, tied with Chicago and LA for the highest of any major US city. See how it stacks up against NYC, SF, Houston, and Portland.
Read article
Agentic ROI Blueprint: Replacing Roles in 2026
In 2026, teams are measuring total capability, not just headcount. Learn how to model the cost of replacing or augmenting full-time roles with an AI agent stack.
Read articleModern Tools for Every Need
Accurate and Reliable
All calculations run locally. Solve equations with confidence using AI-verified methods.
Verified Precision
Precise Algebraic Calculations Powered by Calculory AI