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If (A+B)^(2)=A^(2)+B^(2) and |A| ne 0 , ...

If `(A+B)^(2)=A^(2)+B^(2)` and `|A| ne 0` , then `|B|=` (where `A` and `B` are matrices of odd order)

A

`2`

B

`-2`

C

`1`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `(A+B)^(2)=A^(2)+B^(2)`
`impliesAB+BA=0`
`impliesAB=-BA`
`implies|AB|=|-BA|`
`implies|A||B|=-|B||A|` (`A` and `B` are odd ordered matices)
`implies|B|=-|B|(|A|=2)`
`implies|B|=0`
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