The inverse of a symmetric matrix is

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

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

The inverse of $\begin{bmatrix} 2 & -3 \\ -4 & 2 \end{bmatrix}$ is

If $S = \begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{bmatrix}$ and $A = \frac{1}{2} \begin{bmatrix} b+c & c-a & b-a \\ c-b & c+a & a-b \\ b-c & a-c & a+b \end{bmatrix}$,then $SAS^{-1} =$

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