I need to show that if $A^3=0$, then $I^3−A$ is invertible and its inverse is equal to $I^3+A+A^2$. I have been at this question for almost an hour and do not know how to approach it, any help would be appreciated :)
2026-03-31 14:29:10.1774967350
Show that if a matrix $A$ of order $3×3$ satisfies $A^3=O$, then $I^3−A$ is invertible and its inverse is equal to $I^3+A+A^2.$
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Hint:
Compute $(I^3-A)(I^3+A+A^2)$, from there, you are able to answer the two questions.