If `|(a^2+lambda^2, a b+clambda, ca-blambda), (a b-clambda, b^2+lambda^2, b c+a), (ca+blambda, bc-alambda, c^2+lambda^2)|` `|(lambda, c, -b), (-c,lambda, a), (b,-a,lambda)|=(1+a^2+b^2+c^2)^3` , then he value of `lambda` is
a. `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`