Results 1 to 3 of 3

Math Help - prove that

  1. #1
    Banned
    Joined
    Nov 2009
    Posts
    15

    prove that

    Prove that if A is a non-singular matrix such that A^2 = A, then det(A) = 1?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Quote Originally Posted by westdivo View Post
    Prove that if A is a non-singular matrix such that A^2 = A, then det(A) = 1?

    Hint: for any two square matrices A\,,\, B , det(AB)=det A\cdot detB

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Aug 2009
    From
    Israel
    Posts
    976
    Since A=A^2, we know that det(A^2)=det(A).

    However, det(A^2) = (det(A))^2 for any matrix A. What does this, coupled with A being non-singular, give us?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove a/b and a/c then a/ (3b-7c)
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 23rd 2010, 05:20 PM
  2. prove,,,
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 1st 2010, 09:02 AM
  3. Prove |w + z| <= |w| +|z|
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 28th 2010, 05:44 AM
  4. Replies: 2
    Last Post: August 28th 2009, 02:59 AM
  5. How to prove that n^2 + n + 2 is even??
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 30th 2008, 01:24 PM

Search Tags


/mathhelpforum @mathhelpforum