Question

let a,b,c belongs to R. using the properties of real numbers if ab=1 prove that b=1/a

Answer 1

Given:
\[a,b,c \in \mathbb{R}\]
\[ab=1\]
using the properties of addition:
\[a^{-1}*ab=1*a^{-1}\]
\[\cancel{a^{-1}}\cancel{a}b=1*a^{-1}\]
\[b=a^{-1}\]
which is the same as:
\[b=\frac{1}{a}\]
from the definition of exponentiation (which is a special form of multiplication--which is a special form of addition, which is why we only need to use the properties of addition)
\[QED\]

Answer 2

thanks for your help