Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Why does a real matrix with invertible determinant have to have an inverse?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Similar Threads for Modular arithmetic matrices Date
Modular Arithmetic and Diophantine Equations Oct 25, 2012
Modular arithmetic question about functions Oct 30, 2011
Modular arithmetic Sep 3, 2011
Interesting modular arithmetic problem I found Aug 2, 2011
Modular arithmetic Oct 2, 2008