In the matrix $\begin{bmatrix} -1 & x & 3 \\ -4 & -5 & -6 \\ -7 & y & 9 \end{bmatrix}$, if the cofactors of $-6$ and $-7$ are respectively $22$ and $27$, then $5x + y = $

If $A$ is a $3 \times 3$ matrix and the matrix obtained by replacing the elements of $A$ with their corresponding cofactors is $\begin{bmatrix} 1 & -2 & 1 \\ 4 & -5 & -2 \\ -2 & 4 & 1 \end{bmatrix}$, then a possible value of the determinant of $A$ is

If $A = \begin{bmatrix} 1 & 0 & 2 \\ 2 & 1 & 3 \\ 0 & 3 & -5 \end{bmatrix}$,where $A_{ij}$ is the cofactor of the element $a_{ij}$ of matrix $A$,then $a_{21} A_{21} + a_{22} A_{22} + a_{23} A_{23} = $

If $A = \begin{bmatrix} x & 2 & 1 \\ -2 & y & 0 \\ 2 & 0 & -1 \end{bmatrix}$,where $x$ and $y$ are non-zero real numbers,$\text{trace}(A) = 0$,and $\det(A) = -6$,then the minor of the element $1$ (at position $a_{13}$) of $A$ is:

If the value of a third order determinant is $16$,then the value of the determinant formed by replacing each of its elements by its cofactor is

If $A = \begin{bmatrix} 5 & 6 & 3 \\ -4 & 3 & 2 \\ -4 & -7 & 3 \end{bmatrix}$,then the cofactors of all elements of the second row are respectively: