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:

If in the determinant $\Delta = \begin{vmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{vmatrix}$,$A_1, B_1, C_1$ etc. are the co-factors of $a_1, b_1, c_1$ etc.,then which of the following relations is incorrect?

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:

Let $\alpha \beta \neq 0$ and $A = \begin{bmatrix} \beta & \alpha & 3 \\ \alpha & \alpha & \beta \\ -\beta & \alpha & 2\alpha \end{bmatrix}$. If $B = \begin{bmatrix} 3\alpha & -9 & 3\alpha \\ -\alpha & 7 & -2\alpha \\ -2\alpha & 5 & -2\beta \end{bmatrix}$ is the matrix of cofactors of the elements of $A$,then $\operatorname{det}(AB)$ is equal to.

Match the following elements of the matrix $A = \left[\begin{array}{ccc} 1 & -1 & 0 \\ 0 & 4 & 2 \\ 3 & -4 & 6 \end{array}\right]$ with their co-factors and choose the correct answer.

Element	Co-factor
$A$. $-1$	$(1)$ $-2$
$B$. $1$	$(2)$ $32$
$C$. $3$	$(3)$ $4$
$D$. $6$	$(4)$ $6$
	$(5)$ $-6$

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