Results 1 to 2 of 2

Math Help - One and Two Sided Inverses

  1. #1
    Junior Member
    Joined
    Mar 2010
    Posts
    51

    One and Two Sided Inverses

    I posted a thread not two long ago about one and two sided identities but I'm having a little confusion with inverses. The question is:

    "Prove: Let <A,O> be a system with identity e in which O is associative. If b is a left-inverse for a \in A and c a right-inverse for a, then b = c. As corollaries, show that (a) a two inverse is unique, and (b) if O is commutative, then <A,O> has at most one left inverse."

    I'm sure there is a super simple solution but it isn't immediately apparent to me, thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,454
    Thanks
    1868
    Quote Originally Posted by jameselmore91 View Post
    I posted a thread not two long ago about one and two sided identities but I'm having a little confusion with inverses. The question is:

    "Prove: Let <A,O>
    A is a set of objects, O is a binary operation on them?
    be a system with identity e in which O is associative. If b is a left-inverse for a \in A and c a right-inverse for a, then b = c. As corollaries, show that (a) a two inverse is unique, and (b) if O is commutative, then <A,O> has at most one left inverse."

    I'm sure there is a super simple solution but it isn't immediately apparent to me, thanks in advance.
    By the definition of "left inverse", ba= I, the identity. By the definition of "right inverse", ac= I.

    Mutiply both sides of ac= I, on the left, by b and see what happens. (Using, of course, the fact that O is associative so b(ac)= (ba)c.)

    The last two parts, then, are simple.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. 10 Sided Die
    Posted in the Statistics Forum
    Replies: 7
    Last Post: October 16th 2010, 07:07 PM
  2. sided limit
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 22nd 2009, 11:06 PM
  3. 29-sided die
    Posted in the Statistics Forum
    Replies: 2
    Last Post: July 25th 2009, 08:48 PM
  4. 8 sided die
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: April 5th 2007, 02:48 PM
  5. Six-sided Die
    Posted in the Statistics Forum
    Replies: 5
    Last Post: January 23rd 2007, 06:47 PM

Search Tags


/mathhelpforum @mathhelpforum