Creating tables with spanning rows/columns

I’m trying to create a table which looks like

but I’m not really sure how to incorporate multiple spanning rows and columns together (to add ‘Organism 1’ and ‘Organism 2’). I’ve gotten to this point so far:

documentclass[a4paper,10pt]{article}
usepackage[utf8x]{inputenc}
usepackage{amsmath}

begin{document}
begin{tabular}{r|c|c|}
multicolumn{1}{r}{}
 &  multicolumn{1}{c}{$S$}
 & multicolumn{1}{c}{$T$} cline{2-3}
$S$ & $a,a$ & $b,c$ cline{2-3}
$T$ & $c,b$ & $d,d$ cline{2-3}
end{tabular}

end{document}

And it currently looks like this:

Can anyone suggest how to add the top ‘Organism 2’ and left ‘Organism 1’ row/column entries?

thanks!

documentclass[a4paper,10pt]{article}
usepackage[utf8x]{inputenc}
usepackage{amsmath}
usepackage{multirow}

begin{document}
begin{tabular}{cr|c|c|}
  multicolumn{2}{r}{} & multicolumn{2}{c}{Organism 2} 

  multicolumn{2}{r}{}
 & multicolumn{1}{c}{$S$}
 & multicolumn{1}{c}{$T$} 

  cline{3-4}


  multirow{2}{*}{Organism 1} & $S$ & $a,a$ & $b,c$ 
  cline{3-4}

 & $T$ & $c,b$ & $d,d$ 
  cline{3-4}
end{tabular}

end{document}

documentclass{article}
usepackage{nicematrix}

begin{document}
begin{NiceTabular}{cccc}
                        &     & Block{1-2}{Organism 2} 
                        &     & $S$      & $T$ 
Block{2-1}{Organism 1} & $S$ & Block[hvlines]{2-2}{}
                                $a$, $a$ & $b$, $c$  
                        & $T$ & $c$, $b$ & $d$, $d$ 
end{NiceTabular}
end{document}