A square matrix P satisfies P^(2)=I-P, w...

A square matrix P satisfies `P^(2)=I-P`, where I is identity matrix. If `P^(n)=5I-8P`, then n is :

`4`

`5`

`6`

`7`

Text Solution

Verified by Experts

The correct Answer is:

`(c )` `P^(3)=P(I-P)=P-P^(2)=P-(I-P)=2P-1`
`P^(4)=P(2P-I)=2(I-P)-P=2I-3P`
`P^(5)=P(2I-3P)=2P-3(IP)=5P-3I`
`P^(6)=P(5P-3I)=5(I-P)-3P=5I-8P`
So `n=6`

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