If $3X + 2Y = I$ and $2X – Y = O$, where $ I$  and $ O $ are unit and null matrices of order $3 $ respectively, then

If $F(x)=\left[\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1\end{array}\right],$ show that $F(x) F(y)=F(x+y)$

Let $P = \left[ {\begin{array}{*{20}{c}}
  1&0&0 \\ 
  3&1&0 \\ 
  9&3&1 
\end{array}} \right]$ and $Q = [q_{ij}]$ be two $3\times3$ matrices such that $Q -P^5 = I_3$. Then $\frac{{{q_{21}} + {q_{31}}}}{{{q_{32}}}}$ is equal to

If matrix $A = \left[ {\begin{array}{*{20}{c}}
{\sin \theta }&{\cos ec\theta }&1\\
{\cos ec\theta }&1&{\sin \theta }\\
1&{\sin \theta }&{\cos ec\theta }
\end{array}} \right]$ is a non invertible matrix, then possible value of $'\theta'$ is 

$($ where $n \in I)$

If $A=\left[\begin{array}{rr}3 & 1 \\ -1 & 2\end{array}\right],$ show that $A^{2}-5 A+7 I=0$.