question_answer

Let X be the solution set of the equation \[{{A}^{x}}=I,\] where \[A=\left[ \begin{matrix}    0 & 1 & -1  \\    4 & -3 & 4  \\    3 & -3 & 4  \\ \end{matrix} \right]\] and I is the corresponding unit matrix and \[x\subseteq N,\] then the minimum value of \[\sum{({{\cos }^{x}}\theta +{{\sin }^{x}}\theta ),}\] \[\theta \in R\] is _________.

A)  0                                

B)  1

C)  2        

D)  \[\frac{x\,\,(x+1)}{2}\]

E)  None of these