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If alpha,betane0 and f(n)=alpha^(n)+beta...

If `alpha,betane0` and `f(n)=alpha^(n)+beta^(n)` and
`|(3,1+f(1),1+f(2)),(1+f(1),1+f(2),1+f(3)),(1+f(2),1+f(3),1+f(4))|`
`=k(1-alpha)^(2)(1-beta)^(2)(alpha-beta)^(2)` then k is equal to

A

`(1)/(alphabeta)`

B

1

C

`-1`

D

`alpha beta`

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The correct Answer is:
B
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