Skip to content / Đến nội dung
ThichHocToan.com

1971 AMC 12 Question 6

AMC12 · 1971 AMC 12

Question 6

Let $*$ be a symbol denoting the binary operation on the set $S$ of all nonzero real numbers as follows: for any $a,$ $b\in S,$ $a*b=2ab.$ Which statement is not true?
  1. $*$ is commutative over $S$
  2. $*$ is associative over $S$
  3. $\frac{1}{2}$ is an identity element for $*$ in $S$
  4. Every element of $S$ has an inverse for $*$
  5. $\frac{1}{2a}$ is an inverse for $*$ of the
    element $a$ of $S$