If you are having the Facebook's new Invites layout then the previous 'Select All' code will not function with this. Very very thanks to one of my French friend who got the code which will permit you to choose all your friends at one time and here you will not have to clean then one by one. All you have to do is, just open the Window for invitation and then remove the current URL bar from the top and then paste the below code in that and press enter.
It might take some time to load but you should not worry about that. If you want then you can try the code below.