A) \[-(3{{A}^{2}}+2A+5I)\]
B) \[3{{A}^{2}}+2A+5I\]
C) \[3{{A}^{2}}-2A-5I\]
D) \[(3{{A}^{2}}+2A-5I)\]
Correct Answer: A
Solution :
[a] Let A be a matrix such that \[3{{A}^{3}}+2{{A}^{2}}+5A+I=0\] Post multiply by \[{{A}^{-1}}\] on both the sides, we get \[3{{A}^{3}}{{A}^{-1}}+2{{A}^{2}}{{A}^{-1}}+5A{{A}^{-1}}+I{{A}^{-1}}=0\] \[\Rightarrow 3{{A}^{2}}+2A+5I+{{A}^{-1}}=0\] \[\Rightarrow {{A}^{-1}}=-(3{{A}^{2}}+2A+5I)\]
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