  The study of $n$-dimensional inverted Kloosterman sums was suggested by Katz
(1995) who handled the case when $n=1$ from complex point of view. For general
$n\geq 1$, the $n$-dimensional inverted Kloosterman sums were studied from both
complex and $p$-adic point of view in our previous paper. In this note, we
study the algebraic degree of the inverted $n$-dimensional Kloosterman sum as
an algebraic integer.
