Question: how do i show that for a map {{1,2},{2,1}} there is no nontrivial invariant subspace despite the fact that there is a saddle at x,y=(0,0)

how do i show that for a map {{1,2},{2,1}} there is no nontrivial invariant subspace despite the fact that there is a saddle at x,y=(0,0) so that the fixed point must be invariant

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