Macro for tables that take as arguments the column and row dimensions

Question

I am working with tabulars formatted in a consistent way. Sometimes the tables are 3X3, 3X4, 4X4 etc nXm in general. As it is I have a macro for each of these tables: \matrixIIIC, \matrixIIID etc. Is there a way to define a single macro that would cover all these cases such that as syntax it would look like: \matrix{3}{3}, \matrix{3}{4} etc?

Below is a MWE that shows what I so far have for one of the macros. Ideally, the column and row numbering would also be automatic.

\documentclass{article}

\usepackage{xparse}
\usepackage{multirow}
\usepackage{graphicx}

\DeclareDocumentCommand{\matrixIVD}{ O{RowName} O{ColumnName} }{%
\begin{tabular}{c|*{5}{c|}}
\multicolumn{2}{c}{}  &\multicolumn{4}{c}{#2} \\\cline{3-6}
\multicolumn{1}{c}{}& & a&b&c&d\\\cline{2-6}
\multirow{8}{*}{\rotatebox[origin=c]{90}{#1}} 
&1&&&&\\    
&2&&&&\\
&3&&&&\\    
&4&&&&\\\cline{2-6} 
\end{tabular}%
}%

\begin{document}

\matrixIVD

\end{document}

which produces as output

Oh, and the rowname needs to be automatically centered too!

Answer 1

\documentclass{article}
\usepackage{xparse}
\usepackage{graphicx}

\DeclareDocumentCommand{\zmatrix}{ O{RowName} O{ColumnName} mm}{%
\rotatebox[origin=c]{90}{\hspace{-20pt}#1}%
\kern7pt
\begin{tabular}{|c|*{#3}{c|}}
\multicolumn{1}{c}{} &\multicolumn{#3}{c}{#2} \\\cline{2-\numexpr#3+1\relax}
\multicolumn{1}{c|}{} \mhead{1}{#3}\\\hline
\mrow{1}{#3}{#4}
\hline 
\end{tabular}%
}%

\makeatletter
\def\mhead#1#2{%
\ifnum#1>#2
\expandafter\@gobble
\else
\expandafter\@firstofone
\fi
{&\@alph{#1}\mhead{\numexpr#1+1\relax}{#2}}}


\def\mrow#1#2#3{%
\ifnum#1>#3
\expandafter\@gobble
\else
\expandafter\@firstofone
\fi
{\number#1\mbody{1}{#1}{#2}\\\mrow{\numexpr#1+1\relax}{#2}{#3}}}

\def\mbody#1#2#3{%
\ifnum#1>#3
\expandafter\@gobble
\else
\expandafter\@firstofone
\fi
{&\csname cellX\@alph{#1}X\@alph{#2}\endcsname\mbody{\numexpr#1+1\relax}{#2}{#3}}}

\makeatother 
\begin{document}

\def\cellXaXb{a-b}

\def\cellXcXa{one}
\def\cellXcXb{two}
\def\cellXcXc{three}

\def\cellXdXe{the end}
\zmatrix{4}{5}

\end{document}