Let * represent one of the four basic arithmetic operations such that, for any nonzero real number r,
r * 0 = r and r * r = 0
Which arithmetic operation(s) does the symbol * represent?
A. + only
B. - only
C. + and -
D. X only
E. +, -, or X
If r * o = r, then * represents either addition or subtraction or both. It is also given that r * r = 0. Since r - r = 0 and r + r ≠ 0 when r is not 0, * can represent only subtraction.