The element in the third row and the second c | vedclass

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(A) Step $1$: Find the determinant of matrix $A$.$|A| = 1(4 - 9) - 3(12 - 9) + 3(9 - 3) = 1(-5) - 3(3) + 3(6) = -5 - 9 + 18 = 4$.Step $2$: The element

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$\frac{3}{2}$

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(A) Step $1$: Find the determinant of matrix $A$.$|A| = 1(4 - 9) - 3(12 - 9) + 3(9 - 3) = 1(-5) - 3(3) + 3(6) = -5 - 9 + 18 = 4$.Step $2$: The element in the third row and second column of $A^{-1}$ is given by $\frac{C_{23}}{|A|}$, where $C_{23}$ is the cofactor of the element in the second row and third column of $A$.Step $3$: Calculate the minor $M_{23}$ by deleting the second row and third column: $M_{23} = \begin{vmatrix} 1 & 3 \ 3 & 3 \end{vmatrix} = (3 - 9) = -6$.Step $4$: The cofactor $C_{23} = (-1)^{2+3} M_{23} = -1 	imes (-6) = 6$.Step $5$: The required element is $\frac{C_{23}}{|A|} = \frac{6}{4} = \frac{3}{2}$.

The element in the third row and the second column in the inverse matrix of a matrix $A = \begin{bmatrix} 1 & 3 & 3 \\ 3 & 1 & 3 \\ 3 & 3 & 4 \end{bmatrix}$ is

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