If $A$ and $B$ are symmetric matrices,then $ABA$ is

If $A$ and $B$ are square matrices of the same order and $B$ is a skew-symmetric matrix,then $A^{\prime} B A$ is

Suppose $A$ and $B$ are two square matrices of the same order. If $A$ and $B$ are symmetric matrices, then $AB - BA$ is

If $A$ and $B$ are symmetric matrices of the same order,then $AB - BA$ is . . . . . . .

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

If $A = \begin{bmatrix} 3 & \sqrt{3} & 2 \\ 4 & 2 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & -1 & 2 \\ 1 & 2 & 4 \end{bmatrix}$,verify that $(A+B)^{\prime} = A^{\prime} + B^{\prime}$.