Hello, I had 3 homework problems that I am having trouble with. I really have problems when it comes to proving things. Here goes
Assume A is an n x n invertible matrix. Prove the following identities:
a) adj( A^trace) = [adj(A)]^trace
b) adj( A^-1) = [adj(A)]^-1
c) adj(k*A) = k^(n-1) * adj(A), k E Real Number.
So I've tried a bit, starting out with
A^-1 = 1/det(a) * adj(a) then
A^(-1) * det(a) = adj(a) then I do the trace of both sides and don't really know where to go from there...
[det(a)*A^(-1)]^trace = [adj(A)]^trace
CAn anyone help me out?