sets problems

i have to have an assignment in for thursday, there are two questions i cant get. can anyone help


LetA(R)={αab :R→R, x→ax+b|a,b∈R}(this is the set of so called affine functions from R to R).
(a) Is the composition ◦ a commutative operation on A(R)?
(b) Does A(R) have an identity element with respect to composition?
(c) Which elements, if any, are invertible?

and

Consider the set F3 = {0,1,2}. Define a sum and product on F3 = {0,1,2} so that it becomes a field (i.e., write down an addition and multiplication table as was done in the lecture notes for the finite field with 2 elements, F2). Identify the additive and multiplicative identity elements. For each element, identify its additive inverse. For each nonzero element, identify its multiplicative inverse.


could you tell me how to do them aswell as showing me the answer so i dont have to post up here again with a similar problem.

thanks

LeixlipRed

digan wrote: »

could you tell me how to do them aswell as showing me the answer so i dont have to post up here again with a similar problem.

Eh, how cheeky of you. Read the charter, absolutely no way anyone is going to do these questions for you. If you want help, post up what work you've done on each question and what it is exactly you don't understand. Thank you.

ok, what i dont understand is how you would check for commutativity on such a function. Even just where to start.

thanks

LeixlipRed

Well first of all, it's a set of functions, not a function. The set of all functions that send a vector x to ax + b where a and b are real. So one function could be f(x)=2x+3 another could be g(x)=-x +pi or so on so forth. Do you know how to compose two such functions and do you know what commutativity means?