If the matrix $A$ is both symmetric and skew-symmetric,then

If $A$ is a symmetric matrix,then the matrix $M'AM$ is

If $A=\begin{bmatrix} 1 & 1 & 3 \\ 1 & 7 & 9 \\ 2 & 3 & 7 \end{bmatrix}$,then $\operatorname{Tr}(A^2-A) = $

If the matrix $\begin{bmatrix} a & 2 & -3 \\ b & 0 & 4 \\ c & -4 & 0 \end{bmatrix}$ is a skew-symmetric matrix,then $a+b+c=$

The matrix $A = \begin{bmatrix} i & 1 - 2i \\ -1 - 2i & 0 \end{bmatrix}$ is which of the following?

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