If A is square matrix of order 3 x 3 such that $a_{ij} = j - i$, then which of the following statements are correct?

(A) A is a symmetric matrix.

(B) A is a skew symmetric matrix.

(C) $|A| = 0$.

(D) A is a diagonal matrix.

Choose the correct answer from the options given below:

The system of linear equations $kx + 5y = 5$, $2x + 3y = 5$ will be consistent if

The value of $\begin{vmatrix} 1 & x & y \\ 1 & x+y & y \\ 1 & x & x+y \end{vmatrix}$ is

If $A = \begin{bmatrix} -2 \\ -1 \\ -4 \end{bmatrix}$, $B = [-1 \quad 2 \quad 3]$, then the value of $A'B'$ is

If the matrix $M = \begin{bmatrix} 0 & -1 & 3\alpha \\ 1 & \beta & -5 \\ -6 & 5 & 0 \end{bmatrix}$ is skew-symmetric, then

Let $A = [a_{ij}]$ be a $2 \times 2$ matrix such that $a_{ij} = \frac{|-3i+j|}{2}$ then $a_{21}$ is :

If $0 < x < \pi$ and the matrix $\begin{bmatrix} 4\sin x & -1 \\ -3 & \sin x \end{bmatrix}$ is singular, then the values of $x$ are :