Wolfram Function Repository
Instantuse addon functions for the Wolfram Language
Function Repository Resource:
Give the adjugate matrix of a square matrix
ResourceFunction["Adjugate"][mat] gives the transpose of the cofactor matrix of mat. 
Form the adjugate of a matrix of dimension 2:
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The adjugate is a square matrix of the same dimension:
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The product of the adjugate with the matrix is a diagonal matrix with the same values on the diagonal:
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The values on the diagonal are the determinant of the matrix:
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When a matrix is invertible, the adjugate divided by the determinant gives the inverse:
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The adjugate is defined for symbolic as well as numeric matrices:
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A square matrix need not be invertible:
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This matrix is not invertible because it does not have full rank:
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The adjugate is defined even when the inverse does not exist:
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The adjugate satisfies a simple identity:
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The adjugate and the matrix of minors are the same up to reordering and signs:
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Wolfram Language 11.3 (March 2018) or above
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