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

Let

Since ,

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 .

Hence:

This is where my method goes awry. cannot equal zero or the matrix A is not invertible.

What am I doing wrong??