Which of the following subsets is a subspace of the vector space Fnxn of n x n matrices with coefficients in F? For each of (a), (b) and (c) either prove that the subset is a subspace of Fnxn by verifying all the axioms of the definition, or else, give an example of a matrix (or of matrices) which is (are) in that subset, but which do not verify one of the axioms. (a) Symmetric matrices (A = A¹), (b) Invertible Matrices, (c) Upper triangular matrices.

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