A) \[I-A\]
B) \[{{(I-A)}^{-1}}\]
C) \[{{(I+A)}^{-1}}\]
D) None of these
Correct Answer: B
Solution :
\[{{A}^{3}}=O\] |
\[(I+A+{{A}^{2}})\,\,(I-A)=I-{{A}^{3}}=I\] |
\[\therefore \,\,\,I+A+{{A}^{2}}={{(I-A)}^{-1}}\] |
\[{{A}^{3}}=O\] |
Now \[(I+A+{{A}^{2}})\,\,(I-A)=I-{{A}^{3}}=I\] |
\[\therefore \,\,\,I+A+{{A}^{2}}={{(I-A)}^{-1}}\] |
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