Question: For questions 1 and 2, suppose both A and B are symmetric matrices. 1. Prove that A + B is symmetric. 2. Prove that AB

For questions 1 and 2, suppose both A and B are symmetric matrices. 1. Prove that A + B is symmetric. 2. Prove that AB is symmetric if and only if AB = BA. Be sure to include both implications in the proof. 3. Given A": 3 2 and B": 2 5 find (143)-1. 1 3 3 '2 4. Show workjustifying logically why A = [i 2] is singular. 4 0 0 5. Given the matrix D = [0 2 0] compute both D'1 and D4 003

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