Given a matrix $A = \begin{bmatrix} 0 & 3 & -8 \\ -3 & 0 & 13 \\ 8 & -13 & 0 \end{bmatrix}$. Which of the following statements is/are TRUE?

(A) The matrix A is a skew-symmetric matrix.

(B) The matrix A is a symmetric matrix.

(C) The matrix A is a singular matrix.

(D) The matrix A is a non-singular matrix.

Choose the correct answer from the options given below:

The matrix $X$ in the equation $AX = B$, such that $A = \begin{bmatrix} 1 & 3 \\ 0 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & -1 \\ 0 & 2 \end{bmatrix}$ is given by

The value of $\begin{vmatrix} 1 & a & b+c \\ 1 & b & c+a \\ 1 & c & a+b \end{vmatrix}$ is

If $A = \begin{bmatrix} a & 1 & -1 \\ 0 & b & 4 \\ 4 & 4 & c \end{bmatrix}$ and $abc = 12$, $b = 4a$, then the value of $|A(adjA)|$ is:

The system of equations

$x + ky = 0$

$3x + 5y = 0$

has infinitely many solutions, then k is equal to

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

If $A\begin{bmatrix} 1 & -2 \\ 1 & 4 \end{bmatrix} = \begin{bmatrix} 6 & 0 \\ 0 & 6 \end{bmatrix}$, then matrices $A$ is