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`

Answer

1

Explanation

We observe that the elements in the prefactor are the cofactors of the corresponding elements of the post factor.
Hence L.H.S. `=|(lamda, c, -b),(-c, lamda, a),(b, -a, lamda)|^(3)=[lamda(lamda^(2)+a^(2)+b^(2)+c^(2))]^(3)=(1+a^(2)+b^(2)+c^(2))^(2)implieslamda=1`