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If A and P are different matrices of ord...

If `A` and `P` are different matrices of order `n` satisfying `A^(3)=P^(3)` and `A^(2)P=P^(2)A` (where `|A-P| ne 0`) then `|A^(2)+P^(2)|` is equal to (A) `n` (B) `0` (C) `|A||P|` (D) `|A+P|`

A

`n`

B

`0`

C

`|A||P|`

D

`|A+P|`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `(A^(2)+P^(2))(A-P)=A^(3)-A^(2)P+P^(2)A-P^(3)`
`=(A^(3)-P^(2))+(P^(2)A-A^(2)P)`
`=0`
`:. |(A^(2)+P^(2))(A-P)|=0`
`:. |A^(2)+P^(2)|=0` `( :' |A-P| ne 0)`
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