If `|[a^2+lambda^2,ab+clambda,ca-blambda],[ab-clambda,b^2+lambda^2,bc+aλ],[ca+blambda,bc-alambda,c^2+lambda^2]|``|[λ,c,-b],[-c,λ,a] ,[b,-a,λ]|`=`(1+a^2+b^2+c^2)^3` , then he value of `lambda` is `8` b. `27` c. `1` d. `-1`

Options

A. 8
B. 27
C. 1
D. -1

Answer

C

Explanation

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`