# Homework Help: Show that two representations of permutations from S3 are irreducible

1. Oct 15, 2013

1. The problem statement, all variables and given/known data
Hey everyone,

Let's consider the group S3. We have the following permutations from this group:
$\sigma_{2}=(12)(3), \sigma_{5}=(1,2,3)$

In a two dimensional representation, the matrices for these two permutations are:
http://imageshack.com/a/img543/160/xr2r.jpg [Broken]

I need to show that this representation is irreducible; that there are no proper invariant subspaces.

2. Relevant equations
None that I know of

3. The attempt at a solution
No idea! I need serious help with this one!!

Last edited by a moderator: May 6, 2017