If $A(\operatorname{adj} A)=5 I$ where $I$ is the identity matrix of order $3$,then $|\operatorname{adj} A|$ is equal to

If $A$ is a square matrix of order $4$ and $B = \text{Adj}(A)$,where $|B| = 27$,then the value of $|A^{-1} \text{Adj}(3AB)|$ is,(where $A^{-1}$ denotes the inverse of matrix $A$ and $\text{Adj}(A)$ denotes the adjoint of matrix $A$):

If matrix $A = \begin{bmatrix} x & 3 & 2 \\ 1 & y & 4 \\ 2 & 2 & z \end{bmatrix}$,$xyz = 60$ and $8x + 4y + 3z = 20$,then $A \cdot (\text{Adj } A)$ is equal to

If $A$ is a non-singular matrix such that $(A-2I)(A-4I)=0$,then $A+8A^{-1} = \_\_\_\_$

If $A = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}$,then $A^{-1}$ is given by

Let $A=\left[\begin{array}{ll}x & 1 \\ 1 & 0\end{array}\right]$,$x \in R^{+}$ and $A^4=\left[a_{ij}\right]_2$. If $a_{11}=109$,then $\left(A^4\right)^{-1}=$