If $A$ is a square matrix,then which of the following matrices is not symmetric?

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

Which of the following is an orthogonal matrix?

For the matrix $A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix}$,verify that $(A + A^{\prime})$ is a symmetric matrix.

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