why gcc can link objs with multiple same symbols after ar?

1. why gcc can link objs with multiple same symbols after ar? what's the difference comparing with linking before ar?
2. If multiple same symbols are allowable in linking, then what's the rule to resolve undefined function call(claimed with "extern" before)?

a.c:

extern int f();

int main()
...{
    printf("result is %d ",f());
    return f();
}

int f()
...{
    return 1;
}

 b.c:

int f()
...{
    return 0;
}

test1:

>gcc -c a.c -o a.o

>nm -s a.o

00000030 T f
00000000 t gcc2_compiled.
00000000 T main
                   U printf

>gcc -c b.c -o b.o

>nm -s b.o

00000000 T f
00000000 t gcc2_compiled.

>gcc b.o a.o -o main                                   //link failed because of the same global symbols "f"

a.o: In function `f':
a.o(.text+0x30): multiple definition of `f'
b.o(.text+0x0): first defined here
collect2: ld returned 1 exit status

test2:

>ar cr b.a b.o

f in b.o

b.o:
00000000 T f
00000000 t gcc2_compiled.

>ar cr a.a a.o

Archive index:
main in a.o
f in a.o

a.o:
00000030 T f
00000000 t gcc2_compiled.
00000000 T main
                   U printf

>gcc b.a a.a -o main                              //link is sucessful!!! what's the difference comparing with test1???
> main

result is 1                                                //why is 1???

 

--------------------------------------------------------------------------------------------------------------------------------------------

a1.c:

extern int f();

int main()
...{
    printf("result is %d ",f());
    return f();
}

a2.c:

int f()
...{
    return 1;
}

b.c:

int f()
...{
    return 0;
}

 

> gcc -c a1.c -o a1.o

                   U f
00000000 t gcc2_compiled.
00000000 T main
                   U printf

> gcc -c a2.c -o a2.o

00000000 T f
00000000 t gcc2_compiled.

> gcc -c b.c -o b.o

00000000 T f
00000000 t gcc2_compiled.
> ar cr a2.a a2.o

> nm -s a2.a

Archive index:
f in a2.o

a2.o:
00000000 T f
00000000 t gcc2_compiled.
> ar cr b.a b.o

> nm -s b.a

Archive index:
f in b.o

b.o:
00000000 T f
00000000 t gcc2_compiled.

> ar cr a1.a a1.o

> nm -s a1.a

Archive index:
main in a1.o

a1.o:
                   U f
00000000 t gcc2_compiled.
00000000 T main
                   U printf

> ar cr a.a a2.o a1.o

> nm -s a.a

Archive index:
f in a2.o
main in a1.o

a2.o:
00000000 T f
00000000 t gcc2_compiled.

a1.o:
                   U f
00000000 t gcc2_compiled.
00000000 T main
                  U printf

test1:
> gcc b.a a.a -o main

> main

result is 1

 

test2:

> gcc a1.a b.a a2.a -o main0

> gcc a2.a a1.a b.a -o main0

> main0

result is 0                                                //the result depends on linking sequence!!!

> gcc a1.a a2.a b.a -o main1

> gcc b.a a1.a a2.a -o main1

> main1

result is 1                                               //the result depends on linking sequence!!!

test3:

> gcc b.a a2.a a1.a -main                 //why failed???

a1.a(a1.o): In function `main':
a1.o(.text+0xd): undefined reference to `f'
a1.o(.text+0x25): undefined reference to `f'
collect2: ld returned 1 exit status