If $A = \begin{bmatrix} 1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 3 \end{bmatrix}$ and $B = \operatorname{adj} A$,$C = 5A$,then $\frac{|\operatorname{adj} B|}{|C|} = $

Let $A$ be a $3 \times 3$ matrix such that $\operatorname{adj} A = \begin{bmatrix} 2 & -1 & 1 \\ -1 & 0 & 2 \\ 1 & -2 & -1 \end{bmatrix}$ and $B = \operatorname{adj}(\operatorname{adj} A)$. If $|A| = \lambda$ and $|(B^{-1})^T| = \mu$,then the ordered pair $(|\lambda|, \mu)$ is equal to

If $A$ is a $3 \times 3$ matrix such that $|5 \cdot \text{adj } A| = 5$,then $|A|$ is equal to

The element of the second row and third column in the inverse of $\begin{bmatrix} 1 & 2 & 1 \\ 2 & 1 & 0 \\ -1 & 0 & 1 \end{bmatrix}$ is

If $K \in R_0$,then $\det(adj(KI_n))$ is equal to:

If $A=\left[\begin{array}{cc}1 & 2 \\ -5 & 1\end{array}\right]$ and $A^{-1}=x A+y I$,where $I$ is the unit matrix of order $2$,then the values of $x$ and $y$ are respectively: