Let G be an linear algebraic group, and let H be a zariski dense subgroup of G. Then does H have to be a irreducible subgroup of G? Here H being irreducible means that H has no nontrivial invariant subspaces. Assume that G comes with a faithful irreducible representation. For example we can take G=SL(n,R) or SO(n,R). In these cases subgroup H being irrreducible means that when H acts on R^n there is no nontrivial invariant subspace.