👉 The adjoint of matrix A is often denoted by adj(A). The adjoint of A is the n × n matrix whose (i, j) entry is the (j, i) cofactor of A.Repeat Steps 1, 2 and 3 for all i,j = 1.,n.What you get is called the (i, j)-cofactor of A. Multiply the (i, j)-minor of A by the sign factor (-1) i+j.What you get is called the (i, j)-minor of A. Compute the determinant of this submatrix.What you get is a (n - 1) × (n - 1) submatrix of A. Delete the i-th row and the j-th column of A.To find the adjugate of A, follow these steps: Suppose A is an n × n matrix with real or complex entries. We will freely mix the terms adjoint and adjugate so that you could quickly get used to both of them. This confusion stems from the fact that, in some contexts, the term adjoint can mean the conjugate transpose of a matrix, which is something entirely different from what we consider here. You may also encounter the term classical adjoint matrix. First of all, be aware that what we call the adjoint matrix here is sometimes called the adjugate matrix.
