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Modular arithmetic in matrices

  1. Jul 15, 2010 #1
    This is the question: What must fulfill a matrix to be invertible in module Zn? Demonstrate. Z refers to integers.

    I really appreciate that someone could help me with this because i couldn't find strong information about it.
    I think that considering A as a matrix... the det(A) must be coprime with the module (n), so that gcd(det(A),n)=1 but i'm not sure about it.

    In case that a matrix has inverse in module Zn, is correct to use this to verify?: A.A^-1 mod n = A^-1.A mod n = I ... I = identity matrix
     
    Last edited: Jul 16, 2010
  2. jcsd
  3. Jul 16, 2010 #2
    Hint : What is a unimodular matrix?

    Another hint: A square polynomial matrix U in [itex]\mathbb{R}^{n\times n}[x][/itex] is unimodular if the determinant [itex]\det U \neq 0[/itex] is a constant. The inverse of a unimodular polynomial matrix is again a polynomial matrix.
     
  4. Jul 16, 2010 #3

    Hurkyl

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    Why does a real matrix with invertible determinant have to have an inverse?
     
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