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Question Number 198743 by mnjuly1970 last updated on 23/Oct/23

Answered by witcher3 last updated on 24/Oct/23

$$(\mathrm{A}-\mathrm{I}){(\mathrm{A}-\mathrm{I})}^{-}=\mathrm{I}$$$$=\mathrm{A}(\mathrm{A}-\mathrm{I})-\mathrm{I}{(\mathrm{A}-\mathrm{I})}^{-}=$$$$\mathrm{A}{(\mathrm{A}-\mathrm{I})}^{-}-{(\mathrm{A}-\mathrm{I})}^{-}=\mathrm{I}$$$$\mathrm{tr}\left(\mathrm{A}{(\mathrm{A}-\mathrm{I})}^{-}\right)-\mathrm{tr}{(\mathrm{A}-\mathrm{I})}^{-}=3$$$$\mathrm{tr}\left(\mathrm{A}{(\mathrm{A}-\mathrm{I})}^{-}\right)-8=3$$$$\mathrm{tr}\left(\mathrm{A}{(\mathrm{A}-\mathrm{I})}^{-}\right)=11$$

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