(a) Show that if P is a non-singular nxn matrix then is an eigenvalue of A if and only if, is an eigenvalue of .

(b) Show that if P is a non-singular nxn matrix such that . Show that the only possible eigenvalue for A is . Here is the nxn zero matrix.

For part (a) I think I need to manipulate the expression, here's what I think:

Can anyone help me with part (b)?

I know that lambda must satisfy

we have:

I don't know what to do with this & I'm I'm really stuck here...