Using cofactors of elements of the third column,evaluate $\Delta = \left| \begin{array}{ccc} 1 & x & yz \\ 1 & y & zx \\ 1 & z & xy \end{array} \right|$.

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

Let $A = [a_{ij}] = \begin{bmatrix} \log_5 128 & \log_4 5 \\ \log_5 8 & \log_4 25 \end{bmatrix}$. If $A_{ij}$ is the cofactor of $a_{ij}$,$C_{ij} = \sum_{k=1}^2 a_{ik} A_{jk}$,$1 \leq i, j \leq 2$,and $C = [C_{ij}]$,then $8|C|$ is equal to:

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:

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 $A = \begin{bmatrix} x & 2 & 1 \\ -2 & y & 0 \\ 2 & 0 & -1 \end{bmatrix}$,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: