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1) With some examples I found tha A = -|B|
=> A = B or A = -B or A = B = 0
2) Same as 1) B = -A or B =A or A = B = 0.

So in my opinion 1) & 2) are the same. Hence E.
_________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

From 1) A=-/B/ which means that a) A=B or b)A = -B
from a) A-B=0, from b) A+B=0, adding both equations, 2A=0 so A=0, subtracting both equations gives B=0 so A+B=0. So sufficeint. Similarly statement 2 is also sufficient. So it has to be D. Only 0 suffices the conditions.