From the following, select all statements that are true. There may be more than one correct answer. A, X, and Dare n x n matrices.
A. A is diagonalizable if A = XDX⁻¹ for some diagonal matrix D and some invertible matrix X.
B. If A is diagonalizable, then A is invertible.
C. If there exists a basis for R" consisting entirely of eigenvectors of A, then A is diagonalizable.
D. A is diagonalizable if and only if A has n eigenvalues, counting multiplicities.
E. None of the above.