Consider a matrix P whose only eigenvectors are the multiples of \[\left[ {\begin{array}{*{20}{c}} 1 \\ 4 \end{array}} \right].\]
Consider the following statements:
I. P does not have an inverse.
II. P has a repeated eigen value.
III. P cannot be diagonalized.
Which one of the following options is correct?

A. Only I and III are necessarily true

B. Only II is necessarily true

C. Only I and II are necessarily true

D. Only II and III are necessarily true

Answer: Option D