You run into a problem the moment you want to take e.g. the inverse of a', as a'\inv will yield a double superscript error. This issue annoyed me for many years, and eventually, I created the package SemanTeX to solve this and many other problems. It allows you to type all your math semantically, using keyval syntax, and issues like double superscripts never happen. Here is a code example:
\documentclass{article}
\usepackage{semantex}
\NewVariableClass\MyVar[
output=\MyVar,
definekeys=define keys={
{inv}{ upper=-1 },
},
]
\NewObject\MyVar\va{a} % this means "variable a"
\begin{document}
$ \va[inv] $, $ \va[prime,inv] $, $ \va[prime,spar,inv] $
\end{document}
Following a request from the comments (not to this answer, but to the original question), I provide a macro \inv taking two optional arguments: an optional *, which adds a prime, and an optional argument, which allows you to raise to a negative power other than -1:
\documentclass{article}
\usepackage{xparse}
\NewDocumentCommand\inv{ s O{1} }
{%
\IfBooleanTF{#1}%
{%
^{\prime-#2}%
}%
{%
^{-#2}%
}%
}
\begin{document}
$ a\inv $, $ a\inv[2] $, $ a\inv* $, $ a\inv*[2] $
\end{document}
You can in principle also use a ' instead of a * by replacing { s O{1} } by { t{'} O{1} }. I did not use this approach, as I don’t really find a\inv' to be an intuitive syntax for a'⁻¹ (the inversion and prime are in the opposite order of how they are printed). But that is entirely a matter of personal taste.