# Prove that if the product of $a$ and $b$ has multiplicative inverse modulo $m$

Suppose we have integers $a$,$\space b$ and $m$ with $m \gt 1$. Prove that if the product $a*b$ has a multiplicative inverse modulo m, then so does each of $a$ and $b$.

-

$$1\pmod m=(ab)x=a(bx)=(ax)b$$