1. How to show (prove) the Cayley-Hamilton theorem : “Every matrix is a zero of its characteristic polynomial , Pa(A)=0”. 2. A and B are n-square matrices, show that AB and BA have the same eigenvalues. 3. Show that to say that “ 0is an eigenvalue of linear mapping U” is equivalent to “ U is singular”. 4. Compare eigenvalues of U and eigenvalues of U[upperscript]-1[/upperscript].