Matrix Adjugate (Adjoint) Calculator

Compute the adjugate (classical adjoint) of a square matrix — the transpose of the cofactor matrix — plus its determinant and the inverse relation A⁻¹=adj(A)/det(A).

Input

Enter one matrix row per line; separate entries with spaces or commas (square matrix, up to 6×6).

Matrix A

Result

Determinant det(A)

Size

3×3

Invertibility

Invertible

Adjugate adj(A)

-24	18	5
20	-15	-4
-5	4	1

Since det(A)≠0, the inverse is A⁻¹ = adj(A) / det(A).

How it works

The adjugate adj(A) is the transpose of the cofactor matrix, defined by adj(A)(i,j)=Cⱼᵢ, where Cᵢⱼ is the (i,j) cofactor.
The (i,j) cofactor is Cᵢⱼ=(-1)^(i+j)·Mᵢⱼ, where Mᵢⱼ is the minor: the determinant of the submatrix obtained by deleting row i and column j.
The determinant det(A) is computed via cofactor (Laplace) expansion along the first row.
When det(A)≠0, the inverse is A⁻¹=adj(A)/det(A). When det(A)=0 the matrix is singular and has no inverse.
Enter one matrix row per line, separating entries with spaces or commas. Only square matrices (rows = columns) are supported, up to 6×6.

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