Results 1 to 3 of 3

Math Help - matrix products

  1. #1
    Newbie
    Joined
    Jul 2007
    Posts
    13

    matrix products

    if A and B are n* n matrix, and AB is not equal to BA . and ABA is equal to A^2B; BAB is equal to B^2 A; then prove that A+B is not invertible.
    Last edited by kamaksh_ice; August 25th 2007 at 10:14 PM. Reason: try this!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,245
    Thanks
    1
    I think is not true.
    Let A such that A^2\neq A and B=I_n. Then ABA=A^2\neq BAB=A.
    But A^2B=A^2 and BAB=A and there are not equal.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,657
    Thanks
    598
    Hello, kamaksh_ice!

    Is there a typo in the problem?
    . . The statement is not true . . .


    If A and B are n\times n matrices, and ABA \,\neq \,BAB,

    . . prove that: . A^2B \:=\:B^2A

    Let: . A \:=\:\begin{pmatrix}1&0\\0&1\end{pmatrix},\quad B \:=\:\begin{pmatrix}2&0\\0&2\end{pmatrix}



    \begin{array}{cc}\text{Then:} & ABA \:=\:\begin{pmatrix}1&0\\0&1\end{pmatrix}\begin{pm  atrix}2&0\\0&2\end{pmatrix}\begin{pmatrix}1&0\\0&1  \end{pmatrix}\;=\;\begin{pmatrix}2&0\\0&2\end{pmat  rix} \\ \\<br />
\text{And:} & BAB \:=\:\begin{pmatrix}2&0\\0&2\end{pmatrix}\begin{pm  atrix}1&0\\0&1\end{pmatrix}\begin{pmatrix}2&0\\0&2  \end{pmatrix}\:=\:\begin{pmatrix}4&0\\0&4\end{pmat  rix}\end{array} . . \text{Hence: }\;ABA \:\neq\:BAB



    \begin{array}{cc}\text{But:} & A^2B \:=\:\begin{pmatrix}1&0\\0&1\end{pmatrix}\begin{pm  atrix}1&0\\0&1\end{pmatrix}\begin{pmatrix}2&0\\0&2  \end{pmatrix}\:=\:\begin{pmatrix}2&0\\0&2\end{pmat  rix} \\ \\<br />
\text{And: }& B^2A \:=\:\begin{pmatrix}2&0\\0&2\end{pmatrix}\begin{pm  atrix}2&0\\0&2\end{pmatrix}\begin{pmatrix}1&0\\0&1  \end{pmatrix}\;=\;\begin{pmatrix}4&0\\0&4\end{pmat  rix} \end{array} . . \text{. . . and: }\;A^2B \:\neq \:B^2A



    Ha! red_dog beat me to it ... and explained it better!
    .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. ...norm takes products to products.
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: April 23rd 2010, 08:55 PM
  2. positive definite matrix and inner products
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 2nd 2009, 02:49 AM
  3. Replies: 1
    Last Post: September 7th 2009, 02:51 PM
  4. Inner products
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 4th 2007, 07:36 PM
  5. [SOLVED] matrix products
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: July 7th 2007, 04:21 PM

Search Tags


/mathhelpforum @mathhelpforum