Note: This property holds for square matrices which are invertible.
This property of adjoint of matrices can be easily proved using property
where adj(A) is adjoint of A, det(A) is determinant of A and
is inverse of A. A here is an invertible matrix.
From this property, we can write that
If, we multiply both sides of the equation by A, we get
where I is an identity matrix of same order as of A.
Now taking determinant on both sides of equation. we get
{
}
Dzichi says
how to prove Det(adj(adja))= det(a)^ (n-1)^2 ??????
vipin gupta says
What about case of det(A)=0.
Andres Gamez says
It’s only when A is an invertible matrix, which implies that det(A) is not 0.
whitearwen says
When det = 0 has no inverse matrix
RLS says
This is really good.thank you in advance for your proper guidance.