If A is a square matrix of order 3 such that $|A| = 3$, then the value of $|adj\,A| + |adj\,(adj\,A)|$ is

If the system of equations $x - ky - z = 0, kx - y - z = 0, x + y - z = 0$ has a non-zero solution, then possible values of $k$ are

If $\begin{bmatrix} x-2 & 3 & y \\ -3 & 0 & 2 \\ 4 & z-1 & 0 \end{bmatrix}$ is a skew-symmetric matrix, then the value of $x+y+z$ is:

If A and B are invertible matrices of order 3, $|A| = 2$ and $|(AB)^{-1}| = -\frac{1}{6}$, then the value of $|B|$ is :

If $A=\begin{bmatrix}1 & 2 & 2\\2 & 1 & -2\\\alpha & 2 & \beta\end{bmatrix}$ and $AA^T=9I$, where I is the identity matrix of order 3, then $(\beta-\alpha)$ equals:

If $A = \begin{bmatrix} 1 & 2 \\ 4 & 2 \end{bmatrix}$, then the value of K for which $|2A| = K|A|$ is :

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