Show that if A is invertible and diagonalizable, then A^−1 is diagonalizable. Find a 2 ×2 matrix that is not a diagonal matrix, is not invertible, but is diagonalizable. Alright, I am having some trouble with the first part. So far, I have this: If A is diagnolizable then A=PDP^-1 where P is the matrix who's columns are eigenvectors and D is the diagonal matrix of eigevenvalues of A. (A)^-1=(PDP^-1)^-1 A^-1=PDP^-1 How's that?