If $A = \begin{vmatrix} 5 & 6 & 3 \\ -4 & 3 & 2 \\ -4 & -7 & 3 \end{vmatrix}$,then the cofactors of the elements of the $2^{nd}$ row are:

Find the minors and cofactors of the elements of the determinant $\left|\begin{array}{ccc}2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7\end{array}\right|$ and verify that $a_{11} A_{31}+a_{12} A_{32}+a_{13} A_{33}=0$.

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 cofactors of the elements $3$,$7$ and $6$ of the matrix $\begin{bmatrix} 1 & 2 & 3 \\ 4 & -1 & 7 \\ 2 & 4 & 6 \end{bmatrix}$ are $a$,$b$ and $c$ respectively,then $\begin{bmatrix} a & b & c \end{bmatrix} \begin{bmatrix} 1 \\ 4 \\ 2 \end{bmatrix} + \begin{bmatrix} a & b & c \end{bmatrix} \begin{bmatrix} 3 \\ 7 \\ 6 \end{bmatrix} = $

Write the minors and cofactors of the elements of the following determinant: $\left|\begin{array}{rr}2 & -4 \\ 0 & 3\end{array}\right|$

Sum of minor and co-factor of element $2020$ of $\Delta=\left|\begin{array}{rrr}2019 & 2020 & 2021 \\ 2022 & 2023 & 2024 \\ 2025 & 2026 & 2027\end{array}\right|$ is . . . . . . .