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 non-singular matrix of order $5 \times 5$ and the sum of the elements of each row is $1$, then the sum of the elements of each row in $P^{-1}$ is

If $\begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix} A \begin{bmatrix} -3 & 2 \\ 5 & -3 \end{bmatrix} = I_2$,then $A =$

If a matrix $A$ is such that $3A^3 + 2A^2 + 5A + I = 0$,then its inverse is

Show that the matrix $A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$ satisfies the equation $A^{2} - 4A + I = O$,where $I$ is the $2 \times 2$ identity matrix and $O$ is the $2 \times 2$ zero matrix. Using this equation,find $A^{-1}$.

If $A = \begin{bmatrix} e^t & e^{-t} \cos t & e^{-t} \sin t \\ e^t & -e^{-t} \cos t - e^{-t} \sin t & -e^{-t} \sin t + e^{-t} \cos t \\ e^t & 2e^{-t} \sin t & -2e^{-t} \cos t \end{bmatrix}$,then $A$ is: