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(C) To find the element $a_{23}$ of the inverse matrix $A^{-1}$,we use the formula $a_{ij} = \frac{C_{ji}}{|A|}$,where $C_{ji}$ is the cofactor of the

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$\frac{2}{5}$

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(C) To find the element $a_{23}$ of the inverse matrix $A^{-1}$,we use the formula $a_{ij} = \frac{C_{ji}}{|A|}$,where $C_{ji}$ is the cofactor of the element in the $j$-th row and $i$-th column of matrix $A$.First,calculate the determinant $|A|$:$|A| = 1(4 	imes 7 - 5 	imes 6) - 0(3 	imes 7 - 5 	imes 0) + (-1)(3 	imes 6 - 4 	imes 0)$$|A| = 1(28 - 30) - 0 + (-1)(18 - 0)$$|A| = -2 - 18 = -20$Next,find the cofactor $C_{32}$ of the element at row $3$,column $2$ (which is $6$):$C_{32} = (-1)^{3+2} 	imes 	ext{minor of } 6 = -1 	imes \begin{vmatrix} 1 & -1 \ 3 & 5 \end{vmatrix}$$C_{32} = -1 	imes (1 	imes 5 - (-1) 	imes 3) = -1 	imes (5 + 3) = -8$Finally,$a_{23} = \frac{C_{32}}{|A|} = \frac{-8}{-20} = \frac{2}{5}$.

If matrix $A = \begin{bmatrix} 1 & 0 & -1 \\ 3 & 4 & 5 \\ 0 & 6 & 7 \end{bmatrix}$ and its inverse is denoted by $A^{-1} = \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{bmatrix}$,then the value of $a_{23}$ is:

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