For each of the statements that follow, answer true if the statement is always true and false otherwise. In the case of a true statement, explain or prove your answer. In the case of a false statement, give an example to show that the statement is not always true. Assume that all the given matrices are n × n.
If A ≠ O, but Ak = O (where O denotes the zero matrix) for some positive integer k, then A must be singular.
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