I'm not sure whether \matrixthree{a}{b}{c}{d}{e}{f}{g}{h}{i} is really easier than
\begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix}
Anyway, here's a command with a simpler interface: rows are separated by \\, entries in each row by a comma. The optional argument is for the fences: p (default) for parentheses, b for brackets, v for bars, V for double bars, B for braces. With \buildmatrix[]{1,2\\3,4} you get no delimiter.
\documentclass{article}
\usepackage{amsmath}
\usepackage{xparse}
\ExplSyntaxOn
\NewDocumentCommand{\buildmatrix}{O{p}m}
{
\begin{#1matrix}
% separate the rows and process each row at a time
\seq_set_split:Nnn \l_tmpa_seq { \\ } { #2 }
\seq_map_function:NN \l_tmpa_seq \__nichas_matrix_row:n
\end{#1matrix}
}
\cs_new_protected:Nn \__nichas_matrix_row:n
{
% split the row at commas
\seq_set_split:Nnn \l_tmpb_seq { , } { #1 }
% insert & between each item
\seq_use:Nn \l_tmpb_seq { & }
% end the row
\\
}
\ExplSyntaxOff
\begin{document}
\[
\buildmatrix[b]{a,b,c \\ d,e,f \\ g,h,i }\ne
\buildmatrix{1,2,3,4 \\ 5,6,7,8 \\ 9,10,11,12 \\ 13,14,15,16 }
\]
\end{document}
