Adjoint Of A Matrix Calculator

Work out adjoint of a matrix instantly with clear inputs, formula shown and shareable results.

About Adjoint Of A Matrix Calculator

The adjugate is the transpose of the cofactor matrix. It satisfies A·adj(A) = det(A)·I, which is exactly why the inverse is adj(A) divided by the determinant.

Formula

Adjugate identity

A · adj(A) = det(A) · I, so A⁻¹ = adj(A) / det(A)

Worked example

With the default values below, Adjoint Of A Matrix Calculator returns Adjoint (adjugate) of [-24, 18, 5] [20, -15, -4] [-5, 4, 1]. Change any input above and every figure here is recalculated in your browser.

Inputs used

Square matrix, row by row: 1, 2, 3, 0, 1, 4, 5, 6, 0
Also compute the inverseone of Yes, No: Yes

Results

Adjoint (adjugate): [-24, 18, 5] [20, -15, -4] [-5, 4, 1]
Inverse adj(A)/det(A): [-24, 18, 5] [20, -15, -4] [-5, 4, 1]
Determinant: 1.00000000
Matrix size: 3 by 3

Step by step

1Values used
2Adjugate identity
3Adjoint (adjugate)= [-24, 18, 5] [20, -15, -4] [-5, 4, 1]
4Inverse adj(A)/det(A)= [-24, 18, 5] [20, -15, -4] [-5, 4, 1]
5Determinant= 1.00000000
6Matrix size= 3 by 3

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For [[1,2,3],[0,1,4],[5,6,0]]?

The determinant is 1, so the adjugate and the inverse coincide: [[−24, 18, 5], [20, −15, −4], [−5, 4, 1]].

Is the adjugate defined for singular matrices?

Yes, always. It is the inverse that fails to exist when the determinant is zero.