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How is the adjoint of a matrix formed?

  • A.as the transpose of the matrix of minors
  • B.as the inverse multiplied by the determinant
  • C.as the transpose of the matrix of cofactors
  • D.as the matrix of cofactors without transposing

Answer: C

Correct answer: as the transpose of the matrix of cofactors

Two steps in order: replace each entry by its cofactor - the minor with the sign \( (-1)^{i+j} \) - and then transpose. Omitting the signs gives the matrix of minors, and omitting the transpose gives the cofactor matrix itself; both are offered here. The adjoint earns its place through \( A^{-1} = \mathrm{adj}(A)/|A| \).

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