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

Q: What all properties it is in algebra?

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Calculating dimensions of properties.

Algebra

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George Boole introduced Boolean Algebra in 1847 as a response to an ongoing debate between two mathematicians at the time. Boolean Algebra captures essential properties of both set operations and logic operations.

College Algebra is the required math for all college students.

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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.

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.

properties are based on axioms

Calculating dimensions of properties.

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if you put your mind to it it is not really hard just rember your properties

Algebra

the rules that you have to apply when adding ,subtracting, multiplying or dividing go to this webpage for a proper explanation http://math.about.com/od/algebra/a/distributive.htm

knowing algebra