Abstract Algebra: Groups and Subgroups

[taylor81792]

Homework Statement

The problem says: Suppose that * is an associative binary operation on a set S.
Let H= {a ε S l a * x = x * a for all x ε s}. Show that H is closed under *. ( We think of H as consisting of all elements of S that commute with every element in S)

My teacher is horrible so I am pretty lost in the class. I am aware of what the associative property is, but I'm not sure how to go about solving this question when it comes to the binary operation. This is going to be on my exam so I need to know how to solve it.
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Homework Equations

No relevant equations

The Attempt at a Solution

I know that with associative and groups you would try to prove its isomorphism but I'm not sure where to begin with this one

 

[Joffan]

No isomorphism required...

You're just trying to show that, for any a,b[itex]\in[/itex]H, a*b[itex]\in[/itex]H. You should be able to do this with your definition of H plus associativity.