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JEE Main 1999 Mathematics question on Matrices and Determinants

If f(x)=∣1xx+12xx(x−1)(x+1)x3x(x−1)x(x−1)(x−2)(x+1)x(x−1)∣f(x) = \begin{vmatrix} 1 & x & x+1 \\ 2x & x(x-1) & (x+1)x \\ 3x(x-1) & x(x-1)(x-2) & (x+1)x(x-1) \end{vmatrix}, then f(100)f(100) is equal to
  1. A.
    0
  2. B.
    1
  3. C.
    100
  4. D.
    −100-100
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Correct option: A

[1999]

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