Adjoint (Adjugate) Matrix Calculator

Determinant det(A)Invertible

The determinant of the input matrix. Non-zero means the matrix is invertible.

Adjoint matrix adj(A)24 -12 -2 | 5 3 -5 | -4 2 4

Cofactor matrix C24 5 -4 | -12 3 2 | -2 -5 4

Inverse A⁻¹ = adj(A) / det(A)1.0909 -0.5455 -0.0909 | 0.2273 0.1364 -0.2273 | -0.1818 0.0909 0.1818

Matrix invertible?Yes

det(A)22

Invertible 3x3 matrix: det(A) = 22, adjoint and inverse computed above.

The determinant of your 3x3 matrix is 22.
The inverse A⁻¹ = adj(A) / 22 is shown above. Multiply A by this to recover the identity matrix.
Key identity check: A * adj(A) = 22 * I. Multiply A by adj(A) and you get 22 on every diagonal entry and 0 elsewhere.
The adjoint is found by computing each cofactor C_ij = (-1)^(i+j) * det(submatrix), then transposing the result.

Next stepUse A⁻¹ = adj(A) / 22 to solve the system Ax = b: multiply both sides by A⁻¹ to get x = A⁻¹ b.

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