Build adjoint matrices from cofactors, minors, and determinants. Test square matrices and verify inverse readiness. Clean outputs, exports, and charts support deeper matrix analysis.
Example for a 3 × 3 matrix showing typical analysis outputs.
| Example Matrix | Determinant | Cofactor (1,1) | Adjoint First Row | Inverse Exists |
|---|---|---|---|---|
| [2, 1, 3; 0, 4, 5; 7, 2, 6] | 11 | 14 | [14, 0, -7] | Yes |
| [1, 2, 3; 2, 4, 6; 1, 0, 1] | 0 | 4 | [4, -2, 0] | No |
| [4, 1; 2, 3] | 10 | 3 | [3, -1] | Yes |
For a square matrix A, the adjoint matrix is:
adj(A) = Cof(A)T
Each cofactor is computed by:
Cij = (-1)i+j × det(Mij)
Where Mij is the minor matrix formed by deleting row i and column j.
If the determinant is non-zero, the inverse matrix is:
A-1 = adj(A) / det(A)
The matrix adjoint is the transpose of the cofactor matrix. It is a key intermediate result when finding the inverse of a square matrix using classical adjoint methods.
No. The adjoint is not the inverse by itself. The inverse equals the adjoint divided by the determinant, but only when the determinant is not zero.
Adjoints are defined for square matrices because cofactors, determinants, and inverses all require equal numbers of rows and columns for consistent evaluation.
A zero determinant means the matrix is singular. The adjoint still exists, but the inverse does not because division by zero is impossible.
Yes. It returns the cofactor matrix before transposing it into the adjoint. This helps verify each sign-adjusted minor individually.
Yes. The calculator accepts integers, decimals, and negative numbers. Results are formatted neatly while keeping enough precision for practical matrix work.
The heatmap visualizes the adjoint matrix values. Larger positive and negative entries stand out clearly, making row and column patterns easier to inspect.
Yes. It is useful for study, checking homework, and validating manual calculations because it shows determinant, cofactors, adjoint, inverse status, and exports.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.