$ cat matrix.awk

BEGIN { I=1; OFS="\t" }

NF>1 {
        # If we haven't seen this index before, save its order
        if(! K[$1])
        {
                O[I]=$1;
                K[$1]=I++;
        }

        A[$1, $2]=$3;
}

END {
        for(N=1; N<I; N++)      printf("\t%s", O[N]);
        printf("\n");

        for(N=1; N<I; N++)
        {
                printf("%s", O[N]);

                for(M=1; M<I; M++)
                        printf("\t%s", A[O[N],O[M]]);

                printf("\n");
        }
}

$ cat matrix

aaa aaa 9
aaa bbb 10
aaa ccc 11
aaa ddd 12
bbb aaa 13
bbb bbb 14
bbb ccc 15
bbb ddd 16
ccc aaa 17
ccc bbb 18
ccc ccc 19
ccc ddd 20
ddd aaa 21
ddd bbb 22
ddd ccc 23
ddd ddd 24

$ awk -f matrix.awk < matrix

        aaa     bbb     ccc     ddd
aaa     9       10      11      12
bbb     13      14      15      16
ccc     17      18      19      20
ddd     21      22      23      24

$