I quite often need to use this kind of format for typing up exercises and it is satisfactory but I am wondering how I can align the letter in brackets with the first line of the exercise adjacent to it. So the first question would be how do I accomplish it using gathered inside array and the follow up question would be if there isn't a more appropriate way of accomplishing it.
\documentclass{article}
\usepackage{amssymb,amsmath}
\begin{document}
\noindent \textbf{3.4}
\[
\begin{array}{cccc}
\noindent \textbf{(a)}&
\begin{gathered}
\mathbb{Z}^*_{7}=\left\{1,3,5\right\}\\
4^3=64=1
\end{gathered}&
\noindent \textbf{(b)}&
\begin{gathered}
\mathbb{Z}^*_{8}=\left\{1,3,5,7\right\}\\
3^4=81=1\\
\end{gathered}\\\\
\noindent \textbf{(c)}&
\begin{gathered}
\mathbb{Z}^*_{11}=\left\{1,,2,3,4,5,6,7,8,9,10\right\}\\
\begin{array}{c|cccccccccc}
\cdot & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10\\
\hline
{\rule{0pt}{2.6ex}}
5 & 5 & 10 & 4 & 9 & 3 & 8 & 2 & 7 & 1 & 6\\
\end{array}\\
5^{-2}=5^{-1}\cdot 5^{-1}=9\cdot 9=4\\
\end{gathered}&
\noindent \textbf{(d)}&
\begin{gathered}
\mathbb{Z}^*_{12}=\left\{1,5,7,11\right\}\\
\begin{array}{c|cccc}
\cdot & 1 & 5 & 7 & 11\\
\hline
{\rule{0pt}{2.6ex}}
5 & 5 & 1 & 11 & 7\\
\end{array}\\
5^{-4}\cdot 7^2=5^{-1}\cdot 5^{-1}\cdot 5^{-1}\cdot 5^{-1}\cdot 1=5^4=1\\
\end{gathered}
\end{array}
\]
\end{document}


