If $A$  and $ B$ are square matrices of the same order, then

Let $A$ is a symmetric and $ \,B$ is a skew symmetric matrix, such that  $A – B = \left[ {\begin{array}{*{20}{c}}
  1&2 \\ 
  3&4 
\end{array}} \right]$, then $|A|$ is

Let $A = \left[ {\begin{array}{*{20}{c}}4&6&{ – 1}\\3&0&2\\1&{ – 2}&5\end{array}} \right],B = \left[ {\begin{array}{*{20}{c}}2&4\\0&1\\{ – 1}&2\end{array}} \right]$ and $C = [3\,\,1\,\,2]$. The expression which is not defined is

If $\mathrm{A}=\left[\begin{array}{c}-2 \\ 4 \\ 5\end{array}\right], \mathrm{B}=\left[\begin{array}{lll}1 & 3 & -6\end{array}\right],$ verify that $(\mathrm{AB})^{\prime}=\mathrm{B}^{\prime} \mathrm{A}^{\prime}$.

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