The Adjoint or Reciprocal Determinant arises from A = (a11a22a33 ...a nn) by substituting for each element A ik the corresponding minor Aik so as to form D = (A 11 A 22 A 33 ï¿½ï¿½ï¿½ A nn).
Its value is therefore O n and we have the identity D.0 = A n or D It can now be proved that the first minor of the adjoint determinant, say B rs is equal to An-2aï¿½.
The adjoint determinant is the (n - I) th power of the original determinant.
The adjoint determinant will be seen subsequently to present itself in the theory of linear equations and in the theory of linear transformation.
It is easy to see that the adjoint determinant is also 'symmetrical, viz.