Module 24: question 2 O . Suppose A is an n x n matrix. Which of the below is/are not true? A A matrix A is diagonalizable if and only if A has n distinct eigenvalues. B. A matrix A is diagonalizable if and only if the dimension of each eigenspace of A does not exceed the multiplicity of the corresponding eigenvalue. C. To check if A is diagonalizable, we find the eigenvalues of A and bases for the corresponding eigenspaces where the multiple eigenvalues should be considered first. D If, for at least one multiple eigenvalue of A, the dimension of the eigenspace is less than the multiplicity, A is not diagonalizable; otherwise, A is diagonalizable and we proceed with constructing a diagonalization. E. If A is diagonalizable, we can write A = PDP-1, where D is a diagonal matrix with the eigenvalues of A on its main diagonal that repeat as many times as their multiplicities, and Pis an invertible matrix whose columns are the vectors from the bases for the corresponding eigenspaces. F. To verify that a diagonalization is constructed correctly, we check if the following conditions hold: P is invertible and AP = PD