Two vectors A and B are such that A+B=A-B which one correct stement?

A + B = A - B The rule is you can do any valid operation on both sides of an equation and it will still be equal. Subtract B.

A = A - 2B Subtract A.

0 = -2B Therefore B=0. Now do it again.

A + B = A - B Subtract A.

B = -B Only true when B = 0.

Conclusion: Both a and B are true.

Notes: You need to be more careful about typing things. If you are going to capitalize a list of bullet points, be consistent about it. Read what you have typed to be sure you typed it correctly and the reader will see what you meant to be seen.

Proofread to see if you any words out.