question_answer

Let \[P=\left[ \begin{matrix}    1 & 0 & 0  \\    4 & 1 & 0  \\    16 & 4 & 1  \\ \end{matrix} \right]\] and \[l\] be the identity matrix of order 3. If \[Q=[{{q}_{ij}}]\]  is a matrix, such that \[{{P}^{50}}-Q=I,\] then \[\frac{{{q}_{31}}-{{q}_{32}}}{{{q}_{21}}}\] equals to _______.

A)  103                             

B)  101

C)  201                             

D)  203

E)  None of these