Compute the adjugate of a 2×2 matrix:

Compute the adjugate for a symbolic matrix:

Compute the adjugate for a 3×3 matrix:

Verify the relation with m:

Compute a cofactor using Adjugate:

Verify the function cofactor:

Compute the inverse of a matrix using Adjugate:

Compare with Inverse:

Use Adjugate to solve a linear equation:

Compare with LinearSolve:

Define a function for computing the Gaussian curvature of a surface represented as an implicit Cartesian equation:

The implicit Cartesian equation of a surface with icosahedral symmetry:

Compute its Gaussian curvature:

Visualize regions of positive (red) and negative (blue) Gaussian curvature on the surface:

m.Adjugate[m] is equal to Det[m] times an identity matrix of the same size:

Inverse[m] is equal to the adjugate divided by the determinant:

For an n×n matrix m, Adjugate[m] equals LinearSolve[m,Det[m]IdentityMatrix[n]]:

For an n×n matrix m, Det[Adjugate[m]]==Det[m]^n-1:

Minors[m] can be computed using Adjugate:

The adjugate is defined only for square matrices:

Define a function for computing the adjugate polynomial of a square matrix:

Compute the adjugate polynomial of a matrix:

Evaluating the adjugate polynomial of a matrix at the matrix itself gives the adjugate:

Define a function for computing the iterated adjugate of a square matrix:

Compute the first few iterates for a matrix:

This is equivalent to using NestList with Adjugate: