The definition is permutation matrix. Adjoint matrix is an invariant subspace projection matrix of matrix under permutation, which is an important property of matrix. The definition of adjoint matrix is based on permutation matrix, which represents the exchange between elements. Adjoint matrix is widely used in mathematics, especially in solving linear algebraic problems. The determinant of adjoint matrix is equal to the reciprocal of the determinant of the original matrix, and the trace of adjoint matrix is equal to the value of the determinant of the original matrix plus the trace of the original matrix. In addition, the inverse matrix of adjoint matrix can also be calculated by adjoint matrix, and its formula is that adjoint matrix is divided by determinant of original matrix, so the main property of adjoint matrix is its relationship with determinant and trace of original matrix.