Given the equation: $42x\equiv 1\pmod 5$ I have determined the class $[-2]_{5}$ as $x$ solution of the given equation. Now I have to find the inverse of $x$ (i.e. $x^{-1}=[-2]_5^{-1}$ ). As far as I know, the $x=[-2]_5$ first found is just $[42]_5^{-1}$, and so the inverse of inverse (i.e. $([42]_5^{-1})^{-1}$) is just $42$ again, so $[42]_5=[-2]_5=[x]_5^{-1}$
Am I wrong=