Answer
The multiplicative identity element 1 of the real numbers is unique.
Work Step by Step
Let $a$ be a real number. Suppose both 1 and $b$ are multiplicative identity elements.
$a\cdot 1=a=1\cdot a$
$(b\cdot a)\cdot 1=1\cdot a$, because $b$ is a multiplicative identity element.
$b(a\cdot 1)=1\cdot a$
$b=\frac{1\cdot a}{a\cdot 1}=\frac{a}{a}=1$, so $b=1$. Thus, the multiplicative identity element 1 of the real numbers is unique.
