If $\operatorname{adj} B = A$ and $|P| = |Q| = 1$, then $\operatorname{adj}(Q^{-1} B P^{-1}) = $

Let $A = \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix}$ and $B = I + \operatorname{adj}(A) + (\operatorname{adj} A)^2 + \dots + (\operatorname{adj} A)^{10}$. Then,the sum of all the elements of the matrix $B$ is:

If $A = \begin{bmatrix} 1 & -1 \\ 2 & -1 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 1 \\ 4 & -1 \end{bmatrix}$,then $(A+B)^{-1}$ is

If $A = \begin{bmatrix} \cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \end{bmatrix}$ and $A \text{ adj } A = \begin{bmatrix} k & 0 \\ 0 & k \end{bmatrix}$,then $k$ is equal to :-

Let $A$ be a $n \times n$ matrix such that $A$ is an upper-triangular matrix. Then $adj(A) =$

If $M$ is any square matrix of order $3$ over $\mathbb{R}$ and if $M^{\prime}$ is the transpose of $M$, then $\text{adj}(M^{\prime}) - (\text{adj } M)^{\prime}$ is equal to