$A$ is a matrix of order $3\times 3$. If $A^{\text{'}}=A$ and five entries in the matrix are of one kind and remaining four are of another kind, then the maximum number of such matrices is greater than or equal to

The system of equations
$x-y\cos \theta +z\cos 2\theta =0$

$-x\cos \theta +y-z\cos \theta =0$

$x\cos 2\theta -y\cos \theta +z=0$
has non-trivial solution for $\theta$ equals

Let $A=a_{ij}$ be a matrix of order $3\times 3$ where

$$\begin{gathered} a_{ij}=\left\{\begin{array}{l}x, \mathrm{if} i=j,x\in R \\ 1, \mathrm{if} \left|i-j\right|=1\\ 0, \mathrm{otherwise}\end{array}\right. \end{gathered}$$ 

then which of the following statement(s) is/are true?