1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Tricky algebra proof

  1. Jan 10, 2006 #1
    tricky algebra proof....


    consider the mappings: (R: A-->B)

    Suppose T: C-->A and S: C-->A satisfy RT = RS then T = S
    prove that there exists a; b: B-->A such that bR = idA (identity of A)

    well, im not sure if I can say that b (inverse) = R
    since b maps B to A .. and R maps A to B.... and if i can say that...
    how do i approach the proof?

    I know that RT = RS then T = S.. should i work with this.? using b (inverse)...
    or should i try to see if R or b is injective?....

    ie. b(inverse)T = b(inverse)S ... ??
  2. jcsd
  3. Jan 11, 2006 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    The idea of left cancellable (RS=RT => S=T) is exactly the same as R being injective.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook