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

Find the value of $x,\,y$ and $z$ from the following equation : $\left[\begin{array}{c}x+y+z \\ x+z \\ y+z\end{array}\right]=\left[\begin{array}{l}9 \\ 5 \\ 7\end{array}\right]$

Compute the following : $\left[ {\begin{array}{*{20}{l}}
  {{a^2} + {b^2}}&{{b^2} + {c^2}} \\ 
  {{a^2} + {c^2}}&{{a^2} + {b^2}} 
\end{array}} \right]$ $ + \left[ {\begin{array}{*{20}{c}}
  {2ab}&{2bc} \\ 
  { – 2ac}&{ – 2ab} 
\end{array}} \right]$

If $A = \left[ {\begin{array}{*{20}{c}}{\,\,\,\cos \alpha }&{\sin \alpha }\\{ – \sin \alpha }&{\cos \alpha }\end{array}} \right]$, then ${A^2} = $

If $A\, = \,\left[ {\begin{array}{*{20}{c}}
1&2&x\\
3&{ – 1}&2
\end{array}} \right]$ and $B\, = \,\left[ {\begin{array}{*{20}{c}}
y\\
x\\
1
\end{array}} \right]$ be such that $AB\, = \,\left[ {\begin{array}{*{20}{c}}
6\\
8
\end{array}} \right],$ then