program main1
use module1
implicit none
integer :: i
real,allocatable :: a(:,:)

write(*,*)'Input the size of the square matrix'
read(*,*)i

allocate(a(i,i))
a = function1(i)

write(*,*) 'The square matrix a='
write(*,*) a

deallocate(a)
end program main1

module module1

contains
function function1(i)
real, allocatable,dimension(:,:) :: function1
integer :: i

allocate(function1(i,i))
function1 = 1.0

deallocate(function1)
end function function1
end module

do j=1,i
     write(*,*) a(:,j)
  enddo

1.000  1.000  1.000
  1.000  1.000  1.000
  1.000  1.000  1.000