Is it possible to move/rename files in Git and maintain their history?

Question

I would like to rename/move a project subtree in Git moving it from

/project/xyz

to

/components/xyz

If I

Answer 1

I do:

git mv {old} {new}
git add -u {new}

Answer 2

I make moving the files and then do

git add -A

which put in the sataging area all deleted/new files. Here git realizes that the file is moved.

git commit -m "my message"
git push

I do not know why but this works for me.