A) \[I-A\]
B) \[{{(I+{{A}^{1}})}^{-1}}\]
C) \[{{(I-A)}^{-1}}\]
D) none of these
Correct Answer: C
Solution :
[c] Given \[{{A}^{3}}=0\] Now, \[(I-A)(I+A+{{A}^{2}})\] \[={{I}^{2}}+IA+I{{A}^{2}}-AI-{{A}^{2}}-{{A}^{3}}\] \[=I-{{A}^{3}}=I\] \[\Rightarrow {{(I-A)}^{-1}}=I+A+{{A}^{2}}\]You need to login to perform this action.
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