If $A^5 = O$ such that $A^n ≠ I$ for $1 ≤ n ≤ 4$, then $(I – A)^{–1}$ is equal to
Answer & explanation
Correct answer: option 4
$I-A^5=(I-A)(I+A+A^2+A^3+A^4)$
$I=(I-A)(I+A+A^2+A^3+A^4)$
$⇒(I-A)^{-1}=(I+A+A^2+A^3+A^4)$
If $A^5 = O$ such that $A^n ≠ I$ for $1 ≤ n ≤ 4$, then $(I – A)^{–1}$ is equal to
Correct answer: option 4
$I-A^5=(I-A)(I+A+A^2+A^3+A^4)$
$I=(I-A)(I+A+A^2+A^3+A^4)$
$⇒(I-A)^{-1}=(I+A+A^2+A^3+A^4)$