`Delta= |{:(1,,1+ac,,1+bc),(1,,1+ad,,1+bd),(1,,1+ae,,1+be):}|` is independent of

Options

A. 1
B. 0
C. 3
D. `a + b + c`

Answer

B

Explanation

We have,
`Delta =|(1,1 + ac,1 +bc),(1,1 + ad,1 + bd),(1 ,1 + ac,1 + be)|`
`rArr Delta = |(1,ac,bc),(1,ad,bd),(1,ae,be)|["Applying " C_(2) rarr C_(2) - C_(1),C_(3) rarr C_(3) - C_(1)]`
`rArr Delta = ab |(1,c,c),(1,d,d),(1,e,e)| " " [("Taking a and b common from"),(C_(2) and C_(3) " respectively")]`
`rArr Delta = 0`