Show that the converse to Problem 1 is false by constructing a counterexample. Here, the problem 1 they're referring to is: Let T be a linear operator on V. Prove that if T is non-invertible, then ST and TS are non-invertible.
Added by Carlos O.
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Step 1
To construct a counterexample, we need to find a linear operator T for which both ST and TS are non-invertible, but T is invertible. Let's consider the following counterexample: Let V be a vector space and T be a linear operator on V such that T is invertible. Show more…
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