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

Let $A$ be a skew-symmetric matrix of odd order,then $|A|$ is equal to

If $A = \begin{bmatrix} \cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \end{bmatrix}$,then $A + A^{\prime} = I$,if the value of $\alpha$ is

If $A = \begin{bmatrix} 1 & -1 & 2 \\ -2 & 3 & -3 \\ 4 & -4 & 5 \end{bmatrix}$ is the given matrix and $A^T$ represents the transpose of $A$,then $AA^T - A - A^T =$

Let $X$ and $Y$ be two arbitrary,$3 \times 3$,non-zero,skew-symmetric matrices and $Z$ be an arbitrary $3 \times 3$,non-zero,symmetric matrix. Then which of the following matrices is (are) skew-symmetric?
$(A) Y^3 Z^4 - Z^4 Y^3$
$(B) X^{44} + Y^{44}$
$(C) X^4 Z^3 - Z^3 X^4$
$(D) X^{23} + Y^{23}$

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