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Cofactor Matrix — result sheet
Construct the signed 3x3 cofactor matrix of a finite row-major matrix from its nine 2x2 minors.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Cij = (-1)^(i+j) det(Mij), where Mij is the 2x2 matrix left after deleting row i and column j.
Each cofactor is a signed 2x2 minor. The nine cofactors form a new 3x3 matrix, and first-row expansion of those cofactors also supplies the determinant used by the inverse identity.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- A11 — matrix entry; Row 1, column 1 of matrix A.; minimum -1000; maximum 1000
- A12 — matrix entry; Row 1, column 2 of matrix A.; minimum -1000; maximum 1000
- A13 — matrix entry; Row 1, column 3 of matrix A.; minimum -1000; maximum 1000
- A21 — matrix entry; Row 2, column 1 of matrix A.; minimum -1000; maximum 1000
- A22 — matrix entry; Row 2, column 2 of matrix A.; minimum -1000; maximum 1000
- A23 — matrix entry; Row 2, column 3 of matrix A.; minimum -1000; maximum 1000
- A31 — matrix entry; Row 3, column 1 of matrix A.; minimum -1000; maximum 1000
- A32 — matrix entry; Row 3, column 2 of matrix A.; minimum -1000; maximum 1000
- A33 — matrix entry; Row 3, column 3 of matrix A.; minimum -1000; maximum 1000
Worked example
| Input | Value |
|---|---|
| A11 | 1 |
| A12 | 2 |
| A13 | 3 |
| A21 | 0 |
| A22 | 1 |
| A23 | 4 |
| A31 | 5 |
| A32 | 6 |
| A33 | 0 |
C(A) = [[-24, 20, -5], [18, -15, 4], [5, -4, 1]].
Assumptions and limits
- A is a finite real 3x3 matrix entered in fixed row-major order.
- All entries and every 2x2 minor are required to remain finite within the bounded arithmetic contract.
- The result is the cofactor matrix itself, not its transpose, adjugate, determinant-only value, or inverse.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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