AlgebraFree

Adjoint Matrix Calculator

Compute adjoint matrix for 2x2 or 3x3 numeric grid input.

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Matrix Size

a11

a12

a13

a21

a22

a23

a31

a32

a33

Result

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Formula

Core Formula

\text{adj}(A) = C^T

How it works: Compute cofactors, then transpose to obtain adjoint.

Worked Example

Choose size and enter matrix values to compute adjoint.

The Adjoint (Adjugate) Matrix Explained

The adjoint of a matrix is the transpose of its cofactor matrix. It is a key component in the formula for computing matrix inverses: A inverse = adj(A) / det(A).

Step 1: Compute the cofactor for each entry using the minor determinant and alternating sign
Step 2: Arrange the cofactors into the cofactor matrix
Step 3: Transpose the cofactor matrix to get the adjoint (adjugate)
The adjoint divided by the determinant gives the inverse: A^-1 = adj(A) / det(A)

Note: "adjoint" in this context means "adjugate" (classical adjoint), not the conjugate transpose used in some advanced mathematics contexts.

You can also calculate changes using our Cofactor Matrix Calculator, Inverse Matrix Calculator, Matrix Determinant Calculator or Matrix Transpose Calculator.

Frequently Asked Questions

How is the adjoint used in computing inverses?

The inverse of a matrix A is adj(A) divided by det(A). The adjoint provides the numerator of each entry in the inverse matrix.

Is adjoint the same as transpose?

No. The adjoint is specifically the transpose of the cofactor matrix. A regular transpose just swaps rows and columns without computing cofactors.

Is adjoint the same as adjugate?

Yes. In the context of matrix inverses, adjoint and adjugate refer to the same thing: the transpose of the cofactor matrix. Some fields use "adjoint" to mean conjugate transpose, which is different.

Does every matrix have an adjoint?

Yes. The adjoint can be computed for any square matrix. However, the adjoint only produces a valid inverse when the determinant is nonzero.

How do I add this Adjoint Matrix Calculator to my site?

Absolutely. Use the "Embed" option above to tailor the dimensions, color scheme, and styling to match your site. Copy the generated iframe snippet and drop it into your HTML, WordPress editor, or any CMS. There is no cost and no account required. See calculory.com/services/embed-calculators for a step-by-step walkthrough.

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