Question: (a) Prove that the commutator of two upper triangular matrices is upper triangular. (b) Prove that the commutator of two skew symmetric matrices is skew

(a) Prove that the commutator of two upper triangular matrices is upper triangular.
(b) Prove that the commutator of two skew symmetric matrices is skew symmetric.
(c) Is the commutator of two symmetric matrices symmetric?

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