If Q is orthogonal and A and B are two square matrices so that A =...

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If Q is orthogonal and A and B are two square matrices so that A = QBQT then 1. the eigenvalues of A and B are the same (and so are the determinants and trace), 2. A is symmetric if and only if B is symmetric, 3. A is orthogonal if and only if B is orthogonal. If Q is orthogonal and A and B are two square matrices so that A = QBQT then 1. the eigenvalues of A and B are the same (and so are the determinants and trace), 2. A is symmetric if and only if B is symmetric, 3. A is orthogonal if and only if B is orthogonal.