Question: Problem 1. Prove or disprove. Mark the statements below true or false. If true, provide a brief explanation (one or two lines). If false, find

Problem 1. Prove or disprove. Mark the statements below true or false. If true, provide a brief explanation (one or two lines). If false, find a counterexample. 1. If A, B E Matnxn(F) and im(AB) = im(A), then B is invertible. 2. If A, B E Matnxn(F) and ker(AB) = ker (B), then A is invertible. 3. If A, B E Matnxn(F), then rank(A + B)

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