A) 20
B) 100
C) 10
D) 0
Correct Answer: C
Solution :
Since, \[A\,(adj\,A)=\left[ \begin{matrix} 10 & 0 \\ 0 & 10 \\ \end{matrix} \right]\] ?(i) As we know, \[{{A}^{-1}}=\frac{1}{|A|}adj\,A\] \[\Rightarrow \]\[A\,{{A}^{-1}}|A|=A\,adj\,A\] \[=A(adj\,A)=|A|I\] ?(ii) From Eqs. (i) and (ii), we get \[|A|I=10\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] \[\Rightarrow \] \[|A|I=10I\Rightarrow |A|=10\]You need to login to perform this action.
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