[Solved] Solve the following Prove that if A is n* n matrix, then B=A+A' is symmetric. Prove that if A and B are n* n symmetric matrices, then AB is symmetric


Question: Solve the following

  1. Prove that if \(A\) is \(n\times n\) matrix, then \(B=A+A'\) is symmetric.
  2. Prove that if \(A\) and \(B\) are \(n\times n\) symmetric matrices, then \(AB\) is symmetric if and only if \(AB=BA\).

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