Adjoint Of A Square Matrix

Adjoint of a Square Matrix

Let A = [a_ij]n × n be any n × n matrix. The transpose B′ of the matrix B = [A_ij]n × n, where Aij denotes the cofactor of the element aij in the determinant |A|, is called the adjoint of the matrix A and is denoted by the symbol Adj A.

Thus the adjoint of a matrix A is the transpose of the matrix formed by the

cofactors of A i.e. if

A = then Adj A =

It is easy to see that A(adjA) = (adjA)A = |A|.In.