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A-M-2-2-and-det-A-0-A-3-A-2-A-det-A-2I-




Question Number 213435 by mnjuly1970 last updated on 14/Nov/24
         A ∈ M_(2×2)   ,and ,det (A)≠0 :   A^3  = A^2  + A          ⇒  det ( A −2I )=?
$$ \\ $$$$\:\:\:\:\:\:\:{A}\:\in\:\mathrm{M}_{\mathrm{2}×\mathrm{2}} \:\:,{and}\:,{det}\:\left({A}\right)\neq\mathrm{0}\::\:\:\:{A}^{\mathrm{3}} \:=\:{A}^{\mathrm{2}} \:+\:{A} \\ $$$$\:\:\:\:\:\:\:\:\Rightarrow\:\:{det}\:\left(\:{A}\:−\mathrm{2}{I}\:\right)=? \\ $$$$\:\:\:\:\:\: \\ $$

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