22.  Which of the following statements are NOT correct?

(A) Any linear operator on an n-dimensional vector space that has fewer than n distinct eigenvalues is not diagonalizable. 

(B) Two distinct eigenvectors corresponding to the same eigenvalue are always linearly independent.

(C) If A is an eigenvalue of a linear operator T, then each vector in the eigenspace is an eigenvector of T. 

(D) A linear operator 7 on a finite-dimensional vector space is diagonalizable if and only if the multiplicity of each eigenvalue A equals the dimension of the corresponding eigenspace . 

(E) If A is diagonalizable, then   is also diagonalizable.