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If A^5=O such that A^n != I for 1 <= n <...

If `A^5=O` such that `A^n != I` for `1 <= n <= 4`, then `(I - A)^-1` is equal to

Text Solution

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We have,
`A^4(I−A)=A^4−A^5`
=`A^4−O=A^4≠I`
=` A^3(l−A)=A^3−A^4≠I`
and,`(I+A)(I−A)=I−A^2≠I`
Hence, `(I−A)−1≠A^4,A^3,I+A.`
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