Question: 1. Determine which of the following operations are associative. Determine which are commutative.  

(a) Operation of \* on Z (integer) defined by a∗b=a−b.  

(b) Operation of \* on R (real numbers) defined by a∗b=a+b+ab.  

(c) Operation of \* on Q (rational) defined by a∗b=a+b/5.  

(d) Operation of \* on Z×Z defined by (a,b)∗(c,d)=(ad+bc, bd).  

(e) Operation of \* on Q^∗ (=Q{0}) defined by a∗b=a/b.

Not asking for the answers but asking which steps should I take or is there a link I can use to understand how to do this. Anything helps!

Answer: 
To prove that the operation $\*$ is commutative, you must show that $a\*b=b\*a$ for all $a$ and $b$. 

If you find $a$ and $b$ such that $a\*b\ne b\*a,$ then you have shown that $\*$ is not commutative.

To prove that $\*$ is associative, you must show that $(a\*b)\*c=a\*(b\*c)$ for all $a,b, $ and $c$. 

If you find $a, b, $ and $c$ such that $(a\*b)\*c\ne a\*(b\*c)$, then the operation $\*$ is not associative.
All you need is to verify the definitions.

For whatever binary operation $\*$, if you can prove that $a\*b=b\*a$ (using general elements, i.e. letters instead of numbers), probably using commutativity of some elementary operations like addition or multiplication or maximum, then $\*$ is commutative.   

To prove $\*$ is not commutative, you only need to provide a specific example of $a, b$ (write numbers this time) such that $a\*b\ne b\*a$.

The same goes for associativity.