Caring increases your authority
You need to create relationships with others on the team that are not tied to your respective roles. One day you're going to have difficult conversations with them, and they need to know you cared before that time.
Ask about obvious aspects of their lives, ones they make public and will want to talk about: the figurines on their computer, the book on the corner of their desk, the crazy trainers they're wearing. Even if you don't know about (or like) it, they are all rich conversation starters. Make the effort.
You don't have to pretend to be their friend, to care about things you don't. This is about showing them that they are more than a brain on a seat to you, that you see the person - quirky tastes and all. You might even discover new bands or new comic books you never knew existed.
You're doing it right when they see you coming towards them and they have no idea what you're going to say. If they can predict you're going to talk about schedules, slipppage, or anything that is your responsibility at work, you're not doing it often enough.