Inverse matrix problem

[geouke]

This is my first attempt to use the Lapack library. I am running Lubuntu and compiling with Gfortran. This was my test run:
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module mesquito
implicit none

contains
subroutine inv(matrix, matrix_inv)
real, dimension(:,:), intent(in) :: matrix
real, dimension(size(matrix,1),size(matrix,2)), intent(out) :: matrix_inv
real, dimension(size(matrix,1)) :: work
integer, dimension(size(matrix,1)) :: ipiv
integer :: n, info

external DGETRF
external DGETRI

n = size(matrix,1)
matrix_inv = matrix

print *, matrix
call DGETRF(n, n, matrix_inv, n, ipiv, info)
call DGETRI(n, matrix_inv, n, ipiv, work, n, info)
print *, matrix
end subroutine inv
end module mesquito

program test
use mesquito
implicit none
real, dimension(2,2) :: A, A_inv

A(1,1) = 1; A(1,2) = 2; A(2,1) = 3; A(2,2) = 4
call inv(A, A_inv)

end program test
-----------------------
When I run it I get:

1.00000000 3.00000000 2.00000000 4.00000000 <--- the original matrix [1, 2; 3, 4]
2.00000000 4.00000000 0.00000000 0.00000000 <--- not the original matrix anymore

I did not put my matrix through the subroutines, so I am a bit confused as to why it got changed. Am I overwriting some block of memory it is stored on or something?