Let $A$ be a $n \times n$ matrix such that $|A|=2$. If the determinant of the matrix $\operatorname{Adj}(2 \cdot \operatorname{Adj}(2A^{-1}))$ is $2^{84}$,then $n$ is equal to:

If $A$ is an invertible matrix of order $n$, then the determinant of $\operatorname{adj} A$ is equal to :

If $A$ is a non-zero square matrix of order $n$ with $\det(I+A) \neq 0$ and $A^3=O$, where $I$ and $O$ are the identity and null matrices of order $n \times n$ respectively, then $(I+A)^{-1}$ is equal to

If $A = \begin{bmatrix} 1 & 2 & 3 \\ 1 & 3 & 5 \\ 2 & 1 & 6 \end{bmatrix}$, then $(\operatorname{Adj}(\operatorname{Adj} A))^{-1} =$

Let $A = \begin{bmatrix} 2k - 1 & 1 & 1 \\ 0 & 2k - 1 & 1 \\ 0 & 0 & 2k - 1 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & 2k - 1 & 1 \\ 1 - 2k & 0 & k \\ -1 & -k & 0 \end{bmatrix}$ where $k$ is a real number. If $\det(\text{adj } A) + \det(\text{adj } B) = 11^6$, then the value of $k - 5$ is equal to...

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