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Matrix Inverse — result sheet
Calculate the inverse of a finite row-major 3x3 matrix through the determinant and adjugate identity with stability checks.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: A^-1 = adj(A)/det(A) = transpose(C(A))/det(A), provided |det(A)| exceeds 1e-12 times max(abs(Aij))^3.
The inverse is formed from the transpose of the signed cofactor matrix divided by the determinant. Singular and numerically unstable matrices are rejected before division, and every inverse entry is finite-checked.
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 |
det(A)=1, so A^-1 = [[-24, 18, 5], [20, -15, -4], [-5, 4, 1]].
Assumptions and limits
- A is a finite real 3x3 matrix written in fixed row-major order.
- The determinant must be separated from zero by the documented scale-relative tolerance 1e-12 times the cube of the largest absolute entry.
- The inverse is an algebraic numeric result; no units, conditioning estimate beyond the determinant guard, or downstream solve interpretation is inferred.
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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