If $A = \begin{bmatrix} 3 & 0 & -1 \\ 2 & 3 & 0 \\ 0 & 4 & 1 \end{bmatrix}$, then which of the following is/are correct ?

A. $|A| = 1$

B. $A$ is singular matrix.

C. $|adj A| = 1$

D. $|adj.(adj A)| = 1$

Choose the correct answer from the options given below:

The integral value of k for which the system of linear equations $kx + y + 2z = 0$, $ky = x - 3z$ and $2x + y + kz = 0$ has a non-zero solution is

If $\begin{vmatrix} 2 & 3-x \\ x & 1 \end{vmatrix} = 0$, then the values of $x$ are:

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

If $A=\begin{bmatrix}1&1&1\\1&0&2\\3&1&1\end{bmatrix}$ and $B=\begin{bmatrix}-2&0&2\\5&-2&-1\\1&2&-1\end{bmatrix}$ such that AB=4I (where I is identity matrix) then solution of system of equations $x+y+z=6, x+2z=7, 3x+y+z=12$ is

If $\begin{vmatrix} 1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2a \end{vmatrix} = 86$, then product of all values of $a$ is:

If $A = \begin{bmatrix} 3 & -2 & 3 \\ 2 & 1 & -1 \\ 4 & -3 & 2 \end{bmatrix}$, then the matrix (adj A)A is equal to