Question

If A is a nonsingular matrix such that
A^2 + A - I = 0, what is A^-1?

Solve it . . . . .​

Answer 1

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$\huge\mathcal\purple{Question❔}$

◆ If A is a nonsingular matrix such that A^2 + A - I = 0, what is A^-1?

$\huge\mathcal\purple{Answer✅}$

$=> adj \: A = {A }^{ - 1}$

$\huge\mathbb\pink{Explanation \: ⬇}$

$= {a}^{2} = {a}^{ - 1}$

$= a. {a}^{2} = a.{a}^{ - 1}$

$= {a}^{3} - i$

$= det \: a. {a}^{3} = det \: a.i$

$= det \: a. {a}^{3 } = A. \: adj \: A$

$= det \: A. { A }^{3} = adj \: A$

$=> therefore:$

$= adj \: A = { A}^{ - 1}$

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$\huge\mathbb\blue{Thank \: you \: :)}$

Answer 2

Question:- If A is a nonsingular matrix such that

A^2 + A - I = 0, what is A^-1?

your answer was in the:- attachment ....