Yes. The answer is B. A and B are singular. As an exercise, it would be good to be able to prove this. If, you don't care to work it out for your self, you could highlight the following [between the >>> and <<<] to see a proof.
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Suppose it were true that neither A nor B were the zero matrix and
A B = 0.
If A (B) were non-singular then A-1 (B-1) would exist and we could multiply through by A-1 (B-1) to get B (A) equal to zero. This contradicts the given fact that neither A nor B was the zero matrix and thus A and B are singular.
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