How to increase row height of first row and decrease column width of first column in the table same as the picture I want?

I want to make table as below.

documentclass{article}
usepackage[left=4cm,right=3cm,top=4cm,bottom=3cm]{geometry}
usepackage{amsmath}
usepackage{slashbox}
begin{document}
    begin{table}[h!]
        centering
        caption{$(a_1,b_1)+(a_2,b_2)in boldsymbol{cdot}$}
        begin{tabular}{|c|c|c|c|c|c|}
            hline
            backslashbox{tabular{@{}l@{}}$(a_1,b_1)inboldsymbol{cdot} $endtabular}{$(a_2,b_2)inboldsymbol{cdot}$}&${(0,0)}$&$mathcal{A}_1$&$mathcal{A}_2$&$mathcal{A}_3$&$mathcal{A}_4$
            hline
            ${(0,0)}$&${(0,0)}$&$mathcal{A}_1$&$mathcal{A}_2$&$mathcal{A}_3$&$mathcal{A}_4$
            hline
            $mathcal{A}_1$&$mathcal{A}_1$&${(0,0)},mathcal{A}_4$&$mathcal{A}_3$&$mathcal{A}_2$&$mathcal{A}_1$
            hline
            $mathcal{A}_2$&$mathcal{A}_2$&$mathcal{A}_3$&${(0,0)},mathcal{A}_4$&$mathcal{A}_1$&$mathcal{A}_2$
            hline
            $mathcal{A}_3$&$mathcal{A}_3$&$mathcal{A}_2$&$mathcal{A}_1$&${(0,0)},mathcal{A}_4$&$mathcal{A}_3$
            hline
            $mathcal{A}_4$&$mathcal{A}_4$&$mathcal{A}_1$&$mathcal{A}_2$&$mathcal{A}_3$&${(0,0)},mathcal{A}_4$
            hline
        end{tabular}
        label{tabelbukti15}
    end{table}
end{document}

The result is

Now, I want to increase row height of first row and decrease column width of first column like this picture:

I have tried use this code

documentclass{article}
usepackage[left=4cm,right=3cm,top=4cm,bottom=3cm]{geometry}
usepackage{amsmath}
usepackage{slashbox}
begin{document}
    begin{table}[h!]
        centering
        caption{$(a_1,b_1)+(a_2,b_2)in boldsymbol{cdot}$}
        begin{tabular}{|p{3cm}|c|c|c|c|c|}
            hline
            backslashbox{tabular{@{}l@{}}$(a_1,b_1)inboldsymbol{cdot} $endtabular}{$(a_2,b_2)inboldsymbol{cdot}$}&${(0,0)}$&$mathcal{A}_1$&$mathcal{A}_2$&$mathcal{A}_3$&$mathcal{A}_4$[1cm]
            hline
            ${(0,0)}$&${(0,0)}$&$mathcal{A}_1$&$mathcal{A}_2$&$mathcal{A}_3$&$mathcal{A}_4$
            hline
            $mathcal{A}_1$&$mathcal{A}_1$&${(0,0)},mathcal{A}_4$&$mathcal{A}_3$&$mathcal{A}_2$&$mathcal{A}_1$
            hline
            $mathcal{A}_2$&$mathcal{A}_2$&$mathcal{A}_3$&${(0,0)},mathcal{A}_4$&$mathcal{A}_1$&$mathcal{A}_2$
            hline
            $mathcal{A}_3$&$mathcal{A}_3$&$mathcal{A}_2$&$mathcal{A}_1$&${(0,0)},mathcal{A}_4$&$mathcal{A}_3$
            hline
            $mathcal{A}_4$&$mathcal{A}_4$&$mathcal{A}_1$&$mathcal{A}_2$&$mathcal{A}_3$&${(0,0)},mathcal{A}_4$
            hline
        end{tabular}
        label{tabelbukti15}
    end{table}
end{document}

And the result is not as expected.

How to increase row height of first row and decrease column width of first column in the table same as the picture I want?

documentclass{article}
usepackage[left=4cm,right=3cm,top=4cm,bottom=3cm]{geometry}
usepackage{amsmath}
usepackage{nicematrix}
begin{document}
begin{table}[h!]
centering
caption{$(a_1,b_1)+(a_2,b_2)in boldsymbol{cdot}$}
renewcommand{arraystretch}{1.4}
[begin{NiceArray}{wc{3cm}ccccc}[hvlines]
    rule[-4mm]{0pt}{1.1cm}
    diagbox{(a_1,b_1)inboldsymbol{cdot}}{(a_2,b_2)inboldsymbol{cdot}}&{(0,0)}&mathcal{A}_1&mathcal{A}_2&mathcal{A}_3&mathcal{A}_4
    {(0,0)}&{(0,0)}&mathcal{A}_1&mathcal{A}_2&mathcal{A}_3&mathcal{A}_4
    mathcal{A}_1&mathcal{A}_1&{(0,0)},mathcal{A}_4&mathcal{A}_3&mathcal{A}_2&mathcal{A}_1
    mathcal{A}_2&mathcal{A}_2&mathcal{A}_3&{(0,0)},mathcal{A}_4&mathcal{A}_1&mathcal{A}_2
    mathcal{A}_3&mathcal{A}_3&mathcal{A}_2&mathcal{A}_1&{(0,0)},mathcal{A}_4&mathcal{A}_3
    mathcal{A}_4&mathcal{A}_4&mathcal{A}_1&mathcal{A}_2&mathcal{A}_3&{(0,0)},mathcal{A}_4
end{NiceArray}]
label{tabelbukti15}
end{table}
end{document}

documentclass{article}
usepackage[hmargin={4cm,3cm}, vmargin={4cm,3cm}]{geometry}
usepackage{amsmath}
usepackage[table]{xcolor}

begin{document}
    begin{table}[h!]
caption{$(a_1,b_1)+(a_2,b_2)in boldsymbol{cdot}$}
        label{tabelbukti15}
    centering
    renewcommandarraystretch{1.5}
    vskip-abovedisplayskip
[
begin{array}{|*{6}{c|}}
    hline
    & multicolumn{5}{c|}{(a_2,b_2)inbullet}   
    cline{2-6}
(a_2,b_2)inbullet
    &   {(0,0)}
        &   mathcal{A}_1
            &   mathcal{A}_2
                &   mathcal{A}_3
                    &   mathcal{A}_4           
    hline
{(0,0)}
    &   cellcolor{gray!30}{{(0,0)}}
        &   mathcal{A}_1
            &   mathcal{A}_2
                &   mathcal{A}_3
                    &   mathcal{A}_4           
            hline
mathcal{A}_1
    &   mathcal{A}_1
        &   cellcolor{gray!30}{{(0,0)},mathcal{A}_4}
            &   mathcal{A}_3
                &   mathcal{A}_2
                    &   mathcal{A}_1           
    hline
mathcal{A}_2
    &   mathcal{A}_2
        &   mathcal{A}_3
            &   cellcolor{gray!30}{{(0,0)},mathcal{A}_4}
                &   mathcal{A}_1
                    &   mathcal{A}_2           
    hline
mathcal{A}_3
    &   mathcal{A}_3
        &   mathcal{A}_2
            &   mathcal{A}_1
                &   cellcolor{gray!30}{{(0,0)},mathcal{A}_4}
                    &   mathcal{A}_3           
    hline
mathcal{A}_4
    &   mathcal{A}_4
        &   mathcal{A}_1
            &   mathcal{A}_2
                &   mathcal{A}_3
                    &   cellcolor{gray!30}{{(0,0)},mathcal{A}_4}

    hline
end{array}
]
    end{table}
end{document}