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Mathematics Question on Properties of Determinants

If f(x)f(x) = ∣x+1x1 x(x+1)x(x−1)2x x(x+1)(x−1)x(x−1)(x−2)3x(x−1)∣\begin{vmatrix}x+1&x&1\\\ x\left(x+1\right)&x\left(x-1\right)&2x\\\ x\left(x+1\right)\left(x-1\right)&x\left(x-1\right)\left(x-2\right)&3x\left(x-1\right)\end{vmatrix} , then f(1000)f(1000) is equal to

A

1

B

1000

C

-1000

D

0

Answer

0

Explanation

Solution

Answer (d) 0