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If the orthogonal square matrices A and ...

If the orthogonal square matrices `A` and `B` of same size satisfy `detA+detB=0` then the value of `det(A+B)`

A

`-1`

B

`1`

C

`0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` Since `A` and `B` are orthogonal, det `A=-1`, det `B=1`, or the other way round
Now `A^(T)(A+B)B^(T)=(A+B)^(T)`
We have on taking determinants on both sides
`(detA)det(A+B)detB=det(A+B)`
`implies-det(A+B)=det(A+B)`
`impliesdet(A+B)=0`
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