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Question

Let P be a non-singular matrix such that I+P+P2++Pn=O. Then P1 is equal to

A
P
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B
Pn
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C
Pn1
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D
Pn
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Solution

The correct option is D Pn
I+P+P2++Pn=O (1)
Since, P is non-singular, P1 exists.
Multiplying both sides by P1, we get
P1+I+IP++IPn1=OP1
P1+I(I+P++Pn1)=O
P1=I(I+P+P2++Pn1)
P1=(Pn) [From (1)]
P1=Pn

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