Question: 12. (6 pts.) Recall that Rox is the vector space of n x n matrices. Let S be the subset of Rxn consisting of all

12. (6 pts.) Recall that Rox" is the vector space of n x n matrices. Let S be the subset of Rxn consisting of all singular (i.e., non-invertible) n x n matrices. i. Is S closed under scalar multiplication? Prove this or give a counterexample. ii. Is S closed under addition of matrices? Prove this or give a counterexample. iii. Is S a subspace of Roxn. Justify your

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