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There are so many of them that it is not possible to list them all.

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Q: What all properties it is in algebra?
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What are the properties for pre-algebra?

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How will you remember the properties of Algebra?

There are many different areas within algebra: linear algebra, algebraic structures, algebraic geometry, vector algebra and so on. Some properties are valid in only some of these and not in others. You need to understand what the properties mean and perhaps keep in mind one or two examples where the property is valid.

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Tropical math is a kind of arithmetic and algebra in which addition of two number is their minimum and multiplication is their sum. This has some properties similar to ordinary arithmetic and algebra but other properties are different.

Can algebra properties be used as a reason in a proof?

Yes; In fact, I have found that they are necessary to finish most proofs. I started geometry a couple weeks ago, and so far I have used the Properties of Addition, Subtraction, Multiplication, and Division, the Partition Property, the Reflexive Property, and the Transitive and Substitution Properties. (Not sure if that's all of the algebra properties or not!) Postulates & theorems just aren't enough to solve a lot of problems.

What is the difference between axiom and property in algebra?

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