p(Y)=(-Y)^n + a_(n-1)*Y^(n-1) + ... + a_0
be the characteristic polynomial of matrix A. Show that A is invertible, if and only if a_0 isn't zero and that inverse of A is
where q is polynomial.
So i'm having trouble showing that inverse is polynomial of A.
For the first part i went this way; A is invertible when its determinant isnt zero. p(Y)=det(A-YI), so p(0)=det(A), so det(A)=a_0.
For inverse i dont even know how to start. Any guidance is much appreciated!