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

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:

If $P(\theta) = \begin{bmatrix} 1 & \cot \theta \\ -\cot \theta & 1 \end{bmatrix}$ and $PQ = I$,then find $(\csc^2 \theta)Q$,where $I$ is an identity matrix of order $2 \times 2$.

Find the inverse of the matrix,if it exists: $\left[\begin{array}{ll}2 & -6 \\ 1 & -2\end{array}\right]$

If $A$ and $B$ are non-singular square matrices of the same order,then $adj(AB)$ is equal to:

If for a matrix $A$, $|A|=6$ and $\text{adj } A = \begin{bmatrix} 1 & -2 & 4 \\ 4 & 1 & 1 \\ -1 & k & 0 \end{bmatrix}$, then $k$ is equal to