Adjoint of Matrix

The concept of division is not defined for matrices. In its place, the notion of the inverse of a matrix is introduced. To define the inverse of a matrix, you need the concept of adjoint of a matrix.


Let A= [aij] be a square matrix of order n. Let Aij be the cofactor of aij

Then the nth order matrix [Aij]T is called the adjoint of A. It is denoted by adj A.

Thus, the adj A is the transpose of the cofactor matrix [Aij] of A.


If A is a square matrix of order n, then A(adj A) = |A| In = (adj A)A, where In is the identity matrix of order n.