True or False; Explain

(a)Every n n matrix A is similar to a diagonal matrix D. (b) Every n n matrix A has at least one eigenvector whose corresponding eigenvalue is a real number. (c) If A is an n n matrix, and B is obtained from A by a series of elementary row operations, then A and B have the same eigenvalues. (d) If A is an n n matrix, v is an eigenvector for A, and c is a nonzero real number, then cv is also an eigenvector for A. (e) If A is an n n matrix, and v, w are distinct eigenvectors for A, then v w is also an eigenvector for A

eigenvectors for A, then ~v ~w is also an eigenvector for A