Humans are mammals and elephants are mammals too, but what do elephants have that we don't? What about in the other way round?
Laying eggs is not a characteristic that excludes an animal from being classified as a mammal. So
what you are looking for are characteristics that ONLY mammals have, the platypus has all of the following defining characteristics...
- extensive hair or fur coverage over the surface of its body
- a single piece lower jaw bone
- sweat glands
- produces milk from mammary glands - in the case of the platypus, from openings in the skin rather than the more common teats
- 3 middle ear bones
The defining characteristic of mammals is mammary glands - glands that produce milk for the young. That's where the name mammal comes from. Anything with mammary glands is a mammal, whether it has live birth or lays eggs, and anything without them is NOT a mammal, again whether it has live birth or lays eggs. The platypus has mammary glands and is therefore a mammal.
Bats are mammals. They are warm blooded, and their young are born live. They are basically like little rodents with wings but instead of feathers, they have got fur. But mainly, these birds are considered mammals because of ther mammary glands too.
You are going to be able to compare it with other mammals: