A, P and D are n x n matrices.

Check the true statements below:

O if A is diagonalizable, then A is invertible.

O A is diagonalizable if A = PDP^-1 for some diagonal matrix D and some invertible matrix P.

O A is diagonalizable if and only if A has n eigenvalues, counting multiplicities.

O Is there exits a basis for R^n consisting entirely of eigenvectors of A, then A is diagonalizable.