A) 3
B) 9
C) 12
D) 18
Correct Answer: B
Solution :
[b] \[\det ({{(adj{{A}^{T}})}^{T}})=\det \,(adj\,{{A}^{T}})\] \[={{(\det ({{A}^{T}}))}^{2}}={{(\det \,A)}^{2}}=9\] \[\det \,({{(adj{{A}^{-1}})}^{-1}})=\frac{1}{\det \,\left( adj\,{{A}^{-1}} \right)}\] \[=\frac{1}{{{\left( \det \left( {{A}^{-1}} \right) \right)}^{2}}}={{\left( \det A \right)}^{2}}=9\]
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