Question and Answers Forum

All Questions      Topic List

Arithmetic Questions

Previous in All Question      Next in All Question      

Previous in Arithmetic      Next in Arithmetic      

Question Number 162960 by mnjuly1970 last updated on 02/Jan/22

$$$$$$\mathrm{A}\in {\mathrm{M}}_{n\times n},{\mathrm{A}}^3=\stackrel{-}{\mathrm{O}}$$$$\mathrm{Find},{(\mathrm{A}-2\mathrm{I})}^{-1}=?$$$$$$

Answered by mathmax by abdo last updated on 03/Jan/22

$${\left(2\mathrm{I}\right)}^3-{\mathrm{A}}^3=(2\mathrm{I}-\mathrm{A})({\left(2\mathrm{I}\right)}^2+\left(2\mathrm{I}\right)\mathrm{A}+{\mathrm{A}}^2)=8\mathrm{I}\Rightarrow$$$$(\mathrm{A}-2\mathrm{I})(-\frac{1}{8})(4\mathrm{I}+2\mathrm{A}+{\mathrm{A}}^2)=\mathrm{I}\Rightarrow$$$${(\mathrm{A}-2\mathrm{I})}^{-1}=-\frac{1}{2}\mathrm{I}-\frac{1}{4}\mathrm{A}-\frac{1}{8}{\mathrm{A}}^2$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com