The adjugate or classical adjoint of a matrix A is the transpose of the matrix of cofactors of A. The i, j cofactorAij of A is the scalar
-1
det A
i| j
, where
A
i| j
denotes the matrix that
you obtain from A by removing the ith row and jth column.
Matrices + Adjugate
, adjugate:
Note The product of a matrix with its adjugate is diagonal, with the entries on the diagonal equal to the determinant of the matrix.
Matrices + Adjugate
, adjugate:
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Evaluate
det= 77531
=![]()
Note The relationship just demonstrated gives a formula for the inverse of an invertible matrix A.