Determinant of the Adjoint of a matrix

The adjoint of a square matrix A = [aij]n×n is defined as the transpose of the matrix [Aij]n×n , where Aij is the cofactor of the element aij.

In linear algebra, the adjugate or classical adjoint of a square matrix A, adj(A), is the transpose of its cofactor matrix.

Take determinants on both sides of your A(adjA)=det(A)(I) formula. – Gerry Myerson. Commented Oct 6, 2013 at 2:22.

The determinant of the adjoint of a matrix A is given by |A|n−1 where n is the order of the square matrix. So, for odd n, the determinant is always positive.

The inverse of a matrix is defined as the product of its adjoint divided by the matrix's determinant. In simple terms, a matrix A's inverse is another matrix B ...

Its formula is A-1 = (1/|A|) × adj(A). Here,. |A| = the determinant of A; adj(A) = adjoint of ...

Determinant of the adjoint matrix is equal to the determinant of the matrix raised to power (n-1); which is purely a real number.

The adjoint (or adjugate) of a matrix plays a crucial role in linear algebra, particularly in the calculation of the inverse of a matrix.

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