Computing the cross product of two vectors in Fortran 90

I would like to compute the cross product of two vectors in Fortran 90. For example, in words, the cross product of (1, 2, 3) and (4, 5, 6) turns out to be (-3, 6, -3) in Cartesian coordinates. I wrote the following code (main program followed by function definition):

PROGRAM crosstest
  IMPLICIT NONE

  INTEGER, DIMENSION(3) :: m, n
  INTEGER, DIMENSION(3) :: cross
  INTEGER, DIMENSION(3) :: r

  m=(/1, 2, 3/)
  n=(/4, 5, 6/)
  r=cross(m,n)

END PROGRAM crosstest

FUNCTION cross(a, b)
  INTEGER, DIMENSION(3) :: cross
  INTEGER, DIMENSION(3), INTENT(IN) :: a, b

  cross(1) = a(2) * b(3) - a(3) * b(2)
  cross(2) = a(3) * b(1) - a(1) * b(3)
  cross(3) = a(1) * b(2) - a(2) * b(1)
END FUNCTION cross

But, I get an error message:

crosstest.f90:10.9:

  r=cross(m,n)
         1
Error: Rank mismatch in array reference at (1) (2/1)

where line 10 is r=cross(m,n). It seems that I must be specifying a dimension incorrectly. Here are a few ideas I have:

1. Perhaps the declaration of the function cross in the main program should be simply an integer variable, rather than a 1by3 integer array. So I tried deleting the , DIMENSION(3) in the INTEGER, DIMENSION(3) :: cross line in the main program. But I get an error message:

   crosstest.f90:10.4:
   
     r=cross(m,n)
       1
   Error: The reference to function 'cross' at (1) either needs an
   explicit INTERFACE or the rank is incorrect
   

   so this is even worse, probably.

2. Some (but not all) Fortran function examples on the web place an EXTERNAL statement after the function declaration in the main program. So I tried placing a line EXTERNAL cross after the declaration block in the main program. I get an error message:

   crosstest.f90:8.16:
   
     EXTERNAL cross
                   1
   Error: EXTERNAL attribute conflicts with DIMENSION attribute at (1)
   

   So this seems incorrect also.

3. Some (but not all) Fortran function examples on the web place a RETURN statement on the second-to-last line of the function definition. I tried this, but I get the original rank mismatch error:

   crosstest.f90:10.9:
   
     r=cross(m,n)
            1
   Error: Rank mismatch in array reference at (1) (2/1)
   

   So this does not fix the problem.

Can you please help me see my error?