If $A = \left[ {\begin{array}{*{20}{c}}{\cos \theta }&{ – \sin \theta }\\{\sin \theta }&{\cos \theta }\end{array}} \right]$, then which of the following statements is not correct

If $A',B'$ are transpose matrices of the square matrices $A,B$ respectively , then $(AB)'$is equal to

Find the transpose of the following matrices : $\left[\begin{array}{c}5 \\ \frac{1}{2} \\ -1\end{array}\right]$.

If $A = \left[ {\begin{array}{*{20}{c}}1&2&2\\2&1&{ – 2}\\a&2&b\end{array}} \right]$ is a matrix satisfying the equation $AA^T=9I $ where$ I$ is $3×3$ identity matrix, then the ordered pair $(a, b)$ is equal to:

If $P$ is a $3 \times 3$ matrix such that $P^{\top}=2 P+I$, where $P^{\top}$ is the transpose of $P$ and $I$ is the $3 \times 3$ identity matrix, then there exists a column matrix $X=\left[\begin{array}{l}x \\ y \\ z\end{array}\right] \neq\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$ such that