A) - 2
B) - 1
C) 1
D) 2
Correct Answer: B
Solution :
In \[{{A}^{-1}},\] the element of 2nd row and 3rd column is the \[{{c}_{32}}\] element of the matrix \[({{c}_{ij}})\] of cofactors of element of \[Adj\,(A)=\left[ \begin{matrix} 1 & -2 & 4 \\ 4 & 1 & -2 \\ -2 & 4 & 1 \\ \end{matrix} \right]\], (due to transposition) divided by \[\Delta =\,|A|\,=-2\]. \[\therefore \] Required element =\[\frac{{{(-1)}^{3+2}}{{M}_{32}}}{-2}\,\text{ }=\frac{-(-2)}{-2}=-1\], where \[{{M}_{32}}=\]minor of \[{{c}_{32}}\] in \[Adj\,(A)=\left[ \begin{matrix} 12 & -5 \\ -7 & 3 \\ \end{matrix} \right]\].
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