Customizing the height of the cells in a table

Question

I have the following table construction in LaTeX:

\begin{center}
\begin{minipage}[c]{0.3\textwidth}
\vspace{0pt}
\begin{tabular}[b]{l||c|c|c|c|c|c}
              \textbf{0} & \textbf{1} & \textbf{2} & \textbf{3} & \textbf{4} & \textbf{5} & \textbf{6}\\
\hline 
\hline
\textbf{1}       & $\frac{1}{1}$ & $\frac{1}{2}$ & $\frac{1}{3}$ & $\frac{1}{4}$ & $\frac{1}{5}$ & $\frac{1}{6}$ \\
\hline
\textbf{2}       & $\frac{2}{1}$ & $\frac{2}{2}$ & $\frac{2}{3}$ & $\frac{2}{4}$ & $\frac{2}{5}$ & $\frac{2}{6}$ \\
\hline
\textbf{3}       & $\frac{3}{1}$ & $\frac{3}{2}$ & $\frac{3}{3}$ & $\frac{3}{4}$ & $\frac{3}{5}$ & $\frac{3}{6}$ \\
\hline
\textbf{4}       & $\frac{4}{1}$ & $\frac{4}{2}$ & $\frac{4}{3}$ & $\frac{4}{4}$ & $\frac{4}{5}$ & $\frac{4}{6}$ \\
\hline
\textbf{5}       & $\frac{5}{1}$ & $\frac{5}{2}$ & $\frac{5}{3}$ & $\frac{5}{4}$ & $\frac{5}{5}$ & $\frac{5}{6}$ \\
\hline
\textbf{6}       & $\frac{6}{1}$ & $\frac{6}{2}$ & $\frac{6}{3}$ & $\frac{6}{4}$ & $\frac{6}{5}$ & $\frac{6}{6}$ \\
\end{tabular}
\vspace{0pt}
\end{minipage}
\end{center}

The problem is clear by viewing the following output:

1. How can I modify the height of a cell in table?
2. I know that I can do p{' '} for the width what about the height?

Thanks for all the help!