If $A = \begin{bmatrix} 0 & 3 \\ 2 & 0 \end{bmatrix}$ and $A^{-1} = \lambda (adj(A))$,then $\lambda = $

Let $A$ be a square matrix of order $3$ whose all entries are $1$ and let $I_{3}$ be the identity matrix of order $3$. Then, the matrix $A-3I_{3}$ is

If $A=\begin{bmatrix} \frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ \frac{-2}{\sqrt{5}} & \frac{1}{\sqrt{5}} \end{bmatrix}$,$B=\begin{bmatrix} 1 & 0 \\ i & 1 \end{bmatrix}$,$i=\sqrt{-1}$,and $Q=A^{T}BA$,then the inverse of the matrix $AQ^{2021}A^{T}$ is equal to:

If $B$ is the inverse of a third order matrix $A$ and $\det B = k$,then $(\operatorname{adj}(\operatorname{adj} A))^{-1} =$

If $A = \begin{bmatrix} 1 & \tan x \\ -\tan x & 1 \end{bmatrix}$,then $A^{T} A^{-1} = $

If every element of a square non-singular matrix $A$ of order $n$ is multiplied by $k$ and the new matrix is denoted by $B$,then how are $|A^{-1}|$ and $|B^{-1}|$ related?