Find the minor of element $6$ in the determinant $\Delta = \begin{vmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{vmatrix}$.

If ${A_1}, {B_1}, {C_1}, \dots$ are respectively the co-factors of the elements ${a_1}, {b_1}, {c_1}, \dots$ of the determinant $\Delta = \begin{vmatrix} {a_1} & {b_1} & {c_1} \\ {a_2} & {b_2} & {c_2} \\ {a_3} & {b_3} & {c_3} \end{vmatrix}$,then $\begin{vmatrix} {B_2} & {C_2} \\ {B_3} & {C_3} \end{vmatrix} = $

In the determinant $\left| \begin{array}{ccc} 0 & 1 & -2 \\ -1 & 0 & 3 \\ 2 & -3 & 0 \end{array} \right|$,the ratio of the cofactor to its minor of the element $-3$ is

The sum of the products of the elements of any row of a determinant $A$ with the corresponding co-factors is always equal to

Find the minors and cofactors of the elements $a_{11}$ and $a_{21}$ in the determinant $\Delta = \begin{vmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{vmatrix}$.

The minors of $-4$ and $9$ and the co-factors of $-4$ and $9$ in the determinant $\left| \begin{array}{ccc} -1 & -2 & 3 \\ -4 & -5 & -6 \\ -7 & 8 & 9 \end{array} \right|$ are respectively: