If $A$ is a $3 \times 3$ non-singular matrix and if $|A|=3$,then $|(2A)^{-1}|$ is

If $|A| = 2$,where $A$ is a square matrix of order $4$,then the value of $|Adj(Adj(2A))|$ is (where $Adj(A)$ denotes the adjoint of matrix $A$):

If $P$ is a $3 \times 3$ real matrix such that $P^{T} = aP + (a - 1)I$,where $a > 1$,then $..........$

If $Q$ is the inverse of $A$,where $A = \begin{bmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{bmatrix}$ and $10Q = \begin{bmatrix} 4 & 2 & 2 \\ -5 & 0 & x \\ 1 & -2 & 3 \end{bmatrix}$,find $x$.

$A=\left[\begin{array}{rr}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]$ and $AB=BA=I$,then $B$ is equal to

If $a$ is the determinant of the adjoint of the matrix $A = \begin{bmatrix} 1 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 3 \end{bmatrix}$ and $b$ is the determinant of the inverse of the matrix $B = \begin{bmatrix} 1 & 2 & 3 \\ 4 & -3 & -1 \\ 2 & 1 & -4 \end{bmatrix}$,then find the value of $\frac{b+1}{18b}$.