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Question
If B is a symmetric matrix, write whether the matrix AB AT is symmetric or skew-symmetric.
Solution
If B is a symmetric matrix, then
\[B^T = B\]
`(AB A^T)^T = (A^T) ^T B^T A^T [∵ABC )^T = C^T B^T A^T] `
`( AB A^T )^T = A B^T A^T [∵ ( A^T)^T = A] `
`( AB A^T )^T = AB A^T [∵B^T = B ] `
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