Suppose that we have a m X n matrix A. 1. Show that AA is guaranteed to have nonnegative eigenvalues without making reference to the SVD of A or the matrix ATA. 2. Show that A A has the same rank as A without making reference to the SVD of A or the matrix A A. 3. We start with the SVD A = UEV . Show that expanding A A using this SVD results in the diagonalization of A A. 4. Expand AA using the SVD of A. Show that this results in the diagonalization of AAT