My method is:Suppose that A is a square matrix and is an eigenvalue of A.
(i) Show that is an eigenvalue of for all positive integers n.
(ii) Suppose A is invertible. Show is non-zero and that is an eigenvalue of
I need to show that
which is what I needed to show.
Is this right?
For part 2:
If A is invertible then exists.
Like before .
This is where my method goes awry. cannot equal zero or the matrix A is not invertible.
What am I doing wrong??