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The adjoint of a square matrix A, denoted by adj A, is the transpose of the matrix of cofactors of A. For A=[aij], let Aij denote the cofactor of the entry aij. Then the matrix of cofactors is the matrix [Aij] and adj A=[Aij]T. For example, a 3×3 matrix A and its adjoint can be written In the 2×2 case, a matrix A and its adjoint have the form The adjoint is important because it can be used to find the inverse of a matrix. From the properties of cofactors, it can be shown that A adj A=(det A)I. It follows that, when det  A ≠ 0, the inverse of A is (1/det A) adj A.

Subjects: Mathematics.

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