Solution:
Consider first statement (1) alone.
ab = 2ab.
Or ab = 0.
This means either a = 0 or b = 0 or both a and b are 0.
But the main question says that a is positive.
Or a is not 0.
So b = 0.
Or (1) alone is sufficient to answer the question.
Next consider (2) alone.
It means la+bl = la-bl.
Square both sides.
We get (la+bl)^2 = (la-bl)^2.
Or a^2 + b^2 + 2ab = a^2 + b^2 - 2ab.
Or 4ab = 0.
Or ab = 0.
Using the same reasoning as for statement (1), since a is not 0, b= 0.
So (2) alone is also sufficient to answer the question.

The correct answer is (D).