Results 1 to 4 of 4

Math Help - Proof about square matrix

  1. #1
    Junior Member
    Joined
    Dec 2006
    Posts
    43

    Proof about square matrix

    I found this example in a book of practice problems and if someone could explain this to me, I would be really grateful:

    If all entries of a square matrix A are integers and |A|= + or - 1, show that all entries of A^-1 are integers.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member frenzy's Avatar
    Joined
    Mar 2007
    From
    Planet Express
    Posts
    58
    Quote Originally Posted by buckaroobill View Post
    I found this example in a book of practice problems and if someone could explain this to me, I would be really grateful:

    If all entries of a square matrix A are integers and |A|= + or - 1, show that all entries of A^-1 are integers.
    Adjugate matrix - Wikipedia, the free encyclopedia
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2006
    Posts
    43
    Thanks! So can I just say for the proof that...

    If |A|= +-1, then A^-1 will be comprised of all integers because A is a matrix of cofactor determinants (which are all integers). A determinant of an integer matrix is just an integer because it is the sum of integer products.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member frenzy's Avatar
    Joined
    Mar 2007
    From
    Planet Express
    Posts
    58
    yes
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Matrix that has square root
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 28th 2011, 12:54 PM
  2. Replies: 2
    Last Post: February 19th 2011, 07:57 AM
  3. Determinant of non square matrix
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: March 20th 2008, 09:36 AM
  4. Square matrices within a matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 18th 2008, 11:23 AM
  5. Square of a matrix...
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: February 13th 2007, 10:49 AM

Search Tags


/mathhelpforum @mathhelpforum