If A and B are symmetric matrices of the same order then which of the following statements are correct?

A. AB is symmetric matrix

B. AB - BA is skew symmetric matrix

C. $B^TAB$ is symmetric matrix

D. $A - A^T$ is skew symmetric matrix

Choose the correct answer from the options given below:

If $A$ is a square matrix of order 3 such that $A(adj\,A)=\begin{bmatrix}-3 & 0 & 0\\0 & -3 & 0\\0 & 0 & -3\end{bmatrix}$, then which of the following is NOT correct?

If $A$ is a square matrix of order 3 and $|A|=6$, then the value of $|2A^T|$ is:

The area (in sq. units) of the triangle whose vertices are $(0, 0)$, $(a, 0)$, $(0, b)$, is equal to

The matrix $\begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix}$ is

If $\begin{vmatrix} 2+x & y & z \\ x & 2+y & z \\ x & y & 2+z \end{vmatrix} = 0$, then the value of $x+y+z$ is

If $A = \begin{bmatrix}0 & x & 3\\2 & y & -1\\z & 1 & 0\end{bmatrix}$ is a skew-symmetric matrix, then the value of $3x+y-2z$ is