A) \[\det \,({{A}^{-1}})\]
B) \[\det \,({{B}^{-1}})\]
C) \[\det \,(A)\]
D) \[\det \,(B)\]
Correct Answer: C
Solution :
\[\det \,({{B}^{-1}}AB)\] \[=\det \,({{B}^{-1}})\,detA\,\det B\] \[=\det \,({{B}^{-1}})\,\cdot \det B\,\cdot \det A\] \[=\det \,({{B}^{-1}}B)\,\det A\] \[=\det I\cdot \det A\] \[=1\cdot \det A=\det A\]You need to login to perform this action.
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