The value of a for which the matrix $A = \left( {\begin{array}{*{20}{c}}a&2\\2&4\end{array}} \right)$is singular if

Let $A$ denote the matrix $\left[\begin{array}{ll}0 & i \\ i & 0\end{array}\right]$, where $i^2=-1$, and let $I$ denote the identity matrix $\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$. Then, $I+A+A^2+\ldots+A^{2010}$ is

If $A = \left[ {\begin{array}{*{20}{c}}{ – 1}&0&0\\0&{ – 1}&0\\0&0&{ – 1}\end{array}} \right]$, then ${A^2}$is

Let $A = \left( {\begin{array}{*{20}{c}}0&0&{ – 1}\\0&{ – 1}&0\\{ – 1}&0&0\end{array}} \right)$, the only correct statement about the matrix $A$ is

If $P\left( \theta  \right) = \left[ {\begin{array}{*{20}{c}}  1&{\cot \theta } \\   { – \cot \theta }&1 \end{array}} \right]$ and $PQ$ = $I$, then $\left( {\cos e{c^2}\theta } \right)Q$  (where $I$ is an identity matrix of $2×2$ order)