If \[A=\left[ \begin{matrix} a & b \\ 0 & a \\ \end{matrix} \right]\] is nth root of \[{{I}_{2}}\], then choose the correct statements:(i) if n is odd, \[a=1,\text{ }b=0\](ii) in n is odd, \[a=-1,\text{ }b=0\](iii) if n is even, \[a=1,\text{ }b=0\](iv) if n is even, \[a=-1,\text{ }b=0\]

• A.  i, ii, iii
• B. ii, iii, iv
• C.  i, ii, iii, iv         
• D.  i, iii, iv