If $A = \begin{bmatrix} k & 2 \\ -2 & -k \end{bmatrix}$,then $A^{-1}$ does not exist if $k =$

Let $A$ be a $3 \times 3$ matrix and $\det(A)=2$. If $n = \det(\underbrace{\operatorname{adj}(\operatorname{adj}(\ldots(\operatorname{adj} A)))}_{2024 \text{ times}})$,then the remainder when $n$ is divided by $9$ is equal to

Inverse of the matrix $\left[\begin{array}{cc}0.8 & -0.6 \\ 0.6 & 0.8\end{array}\right]$ is

Let $A$ be any $3 \times 3$ invertible matrix. Then which one of the following is not always true?

If matrix $A = \begin{bmatrix} 3 & 2 & 4 \\ 1 & 2 & -1 \\ 0 & 1 & 1 \end{bmatrix}$ and $A^{-1} = \frac{1}{K} \text{adj}(A)$,then $K$ is:

Let $A = \begin{bmatrix} 1 & 1 & 2 \\ -2 & 0 & 1 \\ 1 & 3 & 5 \end{bmatrix}$. Then the sum of all elements of the matrix $\text{adj}(\text{adj}(2(\text{adj} A)^{-1}))$ is equal to: