I know how to find the adjugate of 3x3 matrix. from the defination. How to find adjugate of 2x2 matrix. e.g A= ( 1 3 ) ______( 2 4 ) adjoint . First . we find matrix of cofactor. from the defination. (n-1)(n-1) matrix * (sign associated with the element's position). Second, we taking the transpose we get the adj(A) Then we find the det(A). Finally, A^-1 = 1/det(A) * adj(A) The inverse of A. [itex]AA^- = A^-A=I[/itex] and A adj(A) = det(A)I The inverse of [itex]A = det(A)I/ A^-[/itex]