題組內容

1 (24) Determine "true" or "false" for the following statements. Briefly sketch your proof when the answer is "true", or give a counterexample when the answer is "false".

b. Let \( A, B \in M_{n \times n}(\mathbb{R}) \). If \( AB = 0 \) then \( \operatorname{rank}(A) + \operatorname{rank}(B) \leq n \).