\left ... \right make different sizes in numerator and denominator

the denominator is set in "cramped" style in which the exponent is lower, which has an effect on the left-right size, it is often best to use manual size \left\right has an adverse effect on horizontal spacing, even when it does not stretch the delimiters. here you could use \bigl\| or simply \|

I simply add a response to generate brackets of the same size. I hope my code is clear. If there are some comments I am available.

\documentclass[a4paper,12pt]{article}
\usepackage{mathtools} 
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
\begin{document}
\[\frac{\norm{A^{-1}}}{\norm{A^{-1}}}\]
\end{document}