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.

Adjoint

Let A= [a_ij] be a square matrix of order n. Let A_ij be the cofactor of a_ij. 

Then the n^th order matrix [A_ij]^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.

Result

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