The number of $3 \times 3$ non- singular matrices, with four entries as $1$ and all other entries as $0$, is 

If $A = \left[ {\begin{array}{*{20}{c}}{ab}&{{b^2}}\\{ – {a^2}}&{ – ab}\end{array}} \right]$ and ${A^n} = O$, then the minimum value of $n$ is

If $A=\left[\begin{array}{cc}0 & -\tan \frac{\alpha}{2} \\ \tan \frac{\alpha}{2} & 0\end{array}\right]$ and $I$ is the identity matrix of order $2,$ show that
$I+A=(I-A)\left[\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right]$

If $A = \left[ {\begin{array}{*{20}{c}}0&1\\1&0\end{array}} \right],B = \left[ {\begin{array}{*{20}{c}}0&{ – i}\\i&0\end{array}} \right]$ then ${(A + B)^2}$ equals

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