Consider the system \[\frac{{dx}}{{dt}} = Ax + Bu\]   with \[A = \left[ {\begin{array}{*{20}{c}} 1&0\\ 0&1 \end{array}} \right]\]   and \[B = \left[ \begin{array}{l} p\\ q \end{array} \right]\]  where p and q are arbitrary real numbers. Which of the following statements about the controllability of the system is true?

A. The system is completely state controllable for any nonzero values of p and q

B. Only p = 0 and q = 0 result in controllability

C. The system is uncontrollable for all values of p and q

D. We cannot conclude about controllability from the given data

Answer: Option C