Let $A$ be a non-singular matrix of order $n$ and $|A|=k$, then $(\operatorname{adj} A)^{-1}$ is

If $A$ and $B$ are non-singular matrices and $\operatorname{det}(AB)=(\operatorname{det} A)(\operatorname{det} B)$,then $((\operatorname{det} A)(\operatorname{det} B)) B^{-1} A^{-1} =$

Let $P=\begin{bmatrix} 3 & -1 & -2 \\ 2 & 0 & \alpha \\ 3 & -5 & 0 \end{bmatrix}$,where $\alpha \in \mathbb{R}$. Suppose $Q=[q_{ij}]$ is a matrix such that $PQ=kI$,where $k \in \mathbb{R}, k \neq 0$ and $I$ is the identity matrix of order $3$. If $q_{23}=-\frac{k}{8}$ and $\det(Q)=\frac{k^2}{2}$,then:

If $A = \begin{bmatrix} 3 & 4 \\ 5 & 7 \end{bmatrix}$,then $A(adj A) = $

Find the inverse of the matrix,if it exists: $\left[\begin{array}{cc}3 & 10 \\ 2 & 7\end{array}\right]$

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: