If $A = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$,then which one of the following statements is not correct?

If $A$ is a square matrix and $A^2+I=2 A$, then $A^9=$

Let $A = \begin{bmatrix} 5 & \sin^2 \theta & \cos^2 \theta \\ -\sin^2 \theta & -5 & 1 \\ \cos^2 \theta & 1 & 5 \end{bmatrix}$. Then the maximum value of $\det(A)$ is

Let $|A|=6$ where $A$ is a $3 \times 3$ matrix. If $|adj(3adj(A^{2} \cdot adj(2A)))|=2^{m} \cdot 3^{n}$, $m, n \in N$, then $m+n$ is equal to:

Let $\omega = - \frac{1}{2} + i\frac{\sqrt{3}}{2}$. Then the value of the determinant $\left| \begin{array}{ccc} 1 & 1 & 1 \\ 1 & -1 - \omega^2 & \omega^2 \\ 1 & \omega^2 & \omega^4 \end{array} \right|$ is

For a $3 \times 3$ matrix $M$,let $\text{trace}(M)$ denote the sum of all the diagonal elements of $M$. Let $A$ be a $3 \times 3$ matrix such that $|A|=\frac{1}{2}$ and $\text{trace}(A)=3$. If $B=\operatorname{adj}(\operatorname{adj}(2A))$,then the value of $|B|+\text{trace}(B)$ equals: