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The characteristic equation of a (3 × 3) matrix P is defined as
α (λ) = |λI – P| = λ3 + λ2 + 2λ + 1 = 0.
If I denotes identity matrix, then the inverse of matrix P will be
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- (P2 + P + 2I)
- (P2 + P + I)
- – (P2 + P + I)
- – (P2 + P + 2I)
Correct Option: D
By Clayey – Hamilton theorem,
Every square matrix satisfies its own characteristic equation
α (λ) = λ 3 + λ2 + 2λ + 1 = 0
α(P) = P3 + P2 + 2P + I = 0
⇒ I = – P3 + P2 + 2P
Premultiplying by p-1, we get
P -1 = – [P2 + P + 2I]
