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Question

The characteristic equation of a 3×3 matrix P is defined as
a(λ)=|λIP|=λ3+λ2+2λ+1=0
If I denotes identify matrix, then the inverse of matrix P will be

A
(P2+P+2I)
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B
(P2+P+1)
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C
(P2+P+I)
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D
(P2+P+2I)
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Solution

The correct option is D (P2+P+2I)
According to Cayley-Hamilton theorem, every square matrix satisfies its own characteristic equation
P3+P2+2P+1=O
Multiplying by matrix [P]1
P2+P+2I+P1=0
P1=(P2+P+2I)

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