Let T be an invertible linear operator on a vector space V . Let U be an invariant vector subspace of V with respect to T. Prove that U is also invariant with respect to T^-1
So, I understand what the first line is saying - that its invertible, so here exists an inverse ie T^-1. In fact, i understand the question, and the answer seems relatively intuitive. Im having problems with formulating a formal proof though. Should I start from the definition of T being invertible?
Since it seems intuitive to me, any hints would be appreciated!