Why did Ava ask Caleb if he wanted to stay?

He's just a means to an end... Supports the idea that she's just a psycho droid, i.e. not human...

If she had said "Stay here!" - he might have realised and reacted faster to get out and wouldn't have been trapped.
If she had said nothing, he would have tried to follow the original plan as fast as possible - to escape with her.

Completely agree! This seems to be one of the most talked about subjects in the movie. After several viewings it's my belief that she was trying to kill him. He was the last obstacle in her escape. Say what you will about him helping her and would have continued blah blah but it's a fact she didn't want him around(Intentionally leaves him behind)because with him she would never be truly free she would always have to pretend to like him and to some degree be subjected. As long as Caleb lived he would be somewhat of a threat. If this weren't the case she would have taken him with her.

So from her view whats the easiest way to kill him. It's already been shown she can't overpower a person and she already exhausted her other robot friend. So does she come at him with a knife or does she continue to manipulate him and convince him to stay in a room while she locks him in.

I've also found Caleb to be a complete moron for waveringly believing she liked him. Do you really think a true AI that wants to escape wouldn't try to manipulate you into letting it loose? To that end do you trust a robot that just killed a man with knife to the chest?