For what values of $x:\left[\begin{array}{lll}1 & 2 & 1\end{array}\right]\left[\begin{array}{lll}1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2\end{array}\right]\left[\begin{array}{l}0 \\ 2 \\ x\end{array}\right]=\mathrm{O} ?$

If $A =$ $\left( {\begin{array}{*{20}{c}}a&b\\c&d\end{array}} \right)$  satisfies the equation $x^2 – (a + d) x + k = 0$, then

If $A = \left[ {\begin{array}{*{20}{c}}i&0\\0&i\end{array}} \right]$ and $B = \left[ {\begin{array}{*{20}{c}}0&{ – i}\\{ – i}&0\end{array}} \right]$, then $(A + B)(A – B)$ is equal to

Let the determinant of a $3 \times 3$ matrix A be 6 then $B$  is a matrix defined by $B = 5{A^2}$. Then det of $B$  is

Construct a $2 \times 2$ matrix, $A=\left[a_{ij}\right]$, whose elements are given by :  $a_{i j}=\frac{i}{j}$.