Here is a solution with {NiceTabular} of nicematrix. That environment is similar to the classical {tabular} (of array) but creates PGF/Tikz nodes under the cells, rows and columns. It's possible to use those nodes to draw whatever rule you want with Tikz in the \CodeAfter.
\documentclass{article}
\usepackage{nicematrix,tikz}
\begin{document}
$\begin{NiceArray}{cccccc}[hvlines-except-borders]
* & a & b & c & d & e \
a & a & b & c & b & d \
b & b & c & a & e & c \
c & c & a & b & b & a \
d & b & e & b & e & d \
e & d & b & a & d & c
\CodeAfter
\tikz \draw [thick, line cap = round] (2-|1) -- (2-|last) (1-|2) -- (last-|2) ;
\end{NiceArray}$
\end{document}
You need several compilations (because nicematrix uses PGF/Tikz nodes under the hood).

With recent version of nicematrix (v. 6.11 of 2022-07-16), it's also possible to define a command (for horizontal rules) and a letter (for vertical rules) with any Tikz charateristic wished.
\documentclass[a4paper,12pt]{article}
\usepackage{nicematrix,tikz}
\begin{document}
\NiceMatrixOptions
{
custom-line =
{
letter = I , % for the vertical rules
command = boldhline , % the horizontal rules
total-width = 1 pt ,
tikz = { line width = 1 pt }
}
}
\begin{NiceTabular}{cIc|c|c|c|c}
$*$ & $a$ & $b$ & $c$ & $d$ & $e$ \\boldhline
$a$ & $a$ & $b$ & $c$ & $b$ & $d$ \\hline
$b$ & $b$ & $c$ & $a$ & $e$ & $c$ \\hline
$c$ & $c$ & $a$ & $b$ & $b$ & $a$ \\hline
$d$ & $b$ & $e$ & $b$ & $e$ & $d$ \\hline
$e$ & $d$ & $b$ & $a$ & $d$ & $c$
\end{NiceTabular}
\end{document}
The output is not exactly the same, because, now, a space is reserved for the width of the rules (both horizontally and vertically).
