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: Matrix determinant question

  1. Apr 13, 2009 #1
    1. The problem statement, all variables and given/known data
    If A is an idempotent matrix (A^2 = A), find all possible values of det(A).

    2. Relevant equations

    3. The attempt at a solution
    I'm not sure if this is the proper way to show it, but here's what I did:

    Since A = A^2, det(A)=det(A^2)
    So det(A) = det(A)*det(A)

    Considering two cases:
    If det(A) is not 0, then
    det(A) = 1.

    The only other way to satisfy det(A) = det(A)*det(A)
    is if det(A) = 0.

    So det(A) is either 1 or 0.
  2. jcsd
  3. Apr 13, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    Sure. If det(A)=x then you have x^2=x so x^2-x=0 so x*(x-1)=0. And, yes, that means x=0 or x=1.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook