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If |a^2+lambda^2a b+clambdac a-blambdaa ...

If `|a^2+lambda^2a b+clambdac a-blambdaa b-clambdab^2+lambda^2b c+a c a+blambdab c-alambdac^2+lambda^2||lambdac-b-clambdaa b-alambda|=(1+a^2+b^2+c^2)^3` , then he value of `lambda` is `8` b. `27` c. `1` d. `-1`

A

8

B

27

C

1

D

-1

Text Solution

Verified by Experts

The correct Answer is:
C
We obserive that the elements in the pre -factor are the cofactors of the corresponding elements of the post factor .Hence
`|{:(lambda,,c,,-b),(-c,,lambda,,a),(b,,-a,,lambda):}|= [lambda (lambda^(2) +a^(2)+b^(2)+c^(2))]^(3) =(1+a^(2)+b^(2)+c^(2))^(3)`
`rArr lambda=1`
Alternate solution:
Writing `a=0, b=0c c=0` on both sides we get
`lambda^(6)lambda^(3) =1" or " lambda=1`
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