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A and B are square matrices such that de...

A and B are square matrices such that det. `(A)=1, B B^(T)=I`, det `(B) gt 0`, and A( adj. A + adj. B)=B.
The value of det `(A+B)` is

A

`-2`

B

`-1`

C

0

D

1

Text Solution

Verified by Experts

The correct Answer is:
D
`B B^(T)=I`
`:. |B B^(T)|=1`
`implies |B||B^(T)|=1`
`implies |B||B^(T)|=1`
`implies |B|=1`
A(adj. A + adj. B)=B
`implies |A|I+Axx"adj "B=B`
`implies I+Axx"adj "B=B`
`implies IxxB+Axx("adj B")xxB=B^(2)`
`implies B+A|B|I=B^(2)`
`implies B+A=B^(2)` (1)
`implies |A+B|=|B|^(2)=1`
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