If $A = \begin{bmatrix} i & 0 \\ 0 & i/2 \end{bmatrix}$ where $i = \sqrt{-1}$,then $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 $A=\begin{bmatrix} 1 & 2 & 2 \\ 3 & 2 & 3 \\ 1 & 1 & 2 \end{bmatrix}$ and $A^{-1}=\begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{bmatrix}$, then $\sum_{1 \leq i, j \leq 3} a_{ij} =$

Let $I$ be the identity matrix of order $3 \times 3$ and for the matrix $A = \begin{bmatrix} \lambda & 2 & 3 \\ 4 & 5 & 6 \\ 7 & -1 & 2 \end{bmatrix}$,$|A| = -1$. Let $B$ be the inverse of the matrix $\operatorname{adj}(A \operatorname{adj}(A^2))$. Then $|\lambda B + I|$ is equal to . . . . . . .

If $A = \begin{bmatrix} 2 & -1 \\ -1 & 2 \end{bmatrix}$ such that $A^2 - 4A + 3I = 0$,where $I$ is a unit matrix of order $2$,then $A^{-1}$ is

If $A$ is a $3 \times 3$ matrix such that $|5 \times \text{adj} A|=5$,then $|A|$ is equal to