1. The problem statement, all variables and given/known data Find the eigenvalues and eigenvectors of A. (Both eigenvalues and eigenvectors are now allowed to be complex.) Is it diagonalizable? Explain why or why not. If it is diagonalizable, explicitly find matrices P and D such that A = PDP−1 where D is a diagonal 2 × 2 matrix. A = [ 0 -i | i 0 ] 3. The attempt at a solution I determined that A cannot be diagonalized because, by the characteristic polynomial equation we get [tex]\lambda[/tex]2 + 1 = 0 Therefore [tex]\lambda[/tex]1 = -i [tex]\lambda[/tex]2 = i plugging [tex]\lambda[/tex]2 into my matrix A I get: ix + iy = 0 -ix + iy = 0 but the only solution to this is x=y=0, I get the same result for [tex]\lambda[/tex]1 Is this correct? I have a feeling this trivial solution is wrong I tried row reduction, but I still get the same result.