1. The problem statement, all variables and given/known data Show that if ker T != 0 then T is not an isomorphism. 2. Relevant equations 3. The attempt at a solution If Ker T != 0 that means that there are multiple solutions for which T=0 meaning it is not injective and hence not isomorphic? Is that correct? I don't think it is, or is there a better way of proving this? Thanks.