• # question_answer If ${{A}^{3}}\,=\,O$, $I\,+\,A\,+\,{{A}^{2}}$quals A) $I\,-\,A$ B) ${{(\,I\,-\,A\,)}^{-1}}$       C) ${{(\,I\,+\,A\,)}^{-1}}$ D) none of these

 ${{A}^{3}}=O$ $(I+A+{{A}^{2}})\,\,(I-A)=I-{{A}^{3}}=I$ $\therefore$      $I+A+{{A}^{2}}={{(I-A)}^{-1}}$ ${{A}^{3}}=O$ now $(I+A+{{A}^{2}})\,\,(I-A)=I-{{A}^{3}}=I$ $\therefore$      $I+A+{{A}^{2}}={{(I-A)}^{-1}}$