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Need some help on how to prove this: Let A and B be two non-zero square matrices of n x n, if AB = 0n, then det(A) and det(B) must both equal to 0. I know if det(AB) = 0, then det(A) or det(B) must be 0, but here the question states that they must both be 0. Appreciate any help, thanks.

Not sure how to prove the following: If U is a subspace of a vector space V, and if u and v are elements of V, but one or both not in U, can u + v be in U? Any help would be appreciated.