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Question Number 198743 by mnjuly1970 last updated on 23/Oct/23
Answered by witcher3 last updated on 24/Oct/23
$$\left(\mathrm{A}−\mathrm{I}\right)\left(\mathrm{A}−\mathrm{I}\right)^{−} =\mathrm{I} \\ $$$$=\mathrm{A}\left(\mathrm{A}−\mathrm{I}\right)−\mathrm{I}\left(\mathrm{A}−\mathrm{I}\right)^{−} = \\ $$$$\mathrm{A}\left(\mathrm{A}−\mathrm{I}\right)^{−} −\left(\mathrm{A}−\mathrm{I}\right)^{−} =\mathrm{I} \\ $$$$\mathrm{tr}\left(\mathrm{A}\left(\mathrm{A}−\mathrm{I}\right)^{−} \right)−\mathrm{tr}\left(\mathrm{A}−\mathrm{I}\right)^{−} =\mathrm{3} \\ $$$$\mathrm{tr}\left(\mathrm{A}\left(\mathrm{A}−\mathrm{I}\right)^{−} \right)−\mathrm{8}=\mathrm{3} \\ $$$$\mathrm{tr}\left(\mathrm{A}\left(\mathrm{A}−\mathrm{I}\right)^{−} \right)=\mathrm{11} \\ $$