If A2 – A + 1 = 0, then the inverse of A is?

Engineering

Mathematics

Special Type of Square Matrices

Inverse of a Matrix

Determination of Function Satisfying The Given Functional Rule

Question

If A² – A + 1 = 0, then the inverse of A is?

I – A

A + I

A – I

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Given,

A² – A + I = 0

⇒ A' – A² = I

multiplying A^–¹ on both sides,

⇒ I – AI = A^–¹

⇒ A^–¹ = I – A

80, the correct option is C.