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Question
If A and B are symmetric matrices, then ABA is
Options
symmetric matrix
skew-symmetric matrix
diagonal matrix
scalar matrix
Solution
symmetric matrix
since A and B are symmetric matrices, we get
` A =A ^' and B =B^' `
\[\left( ABA \right)' = \left( BA \right)' \left( A \right)' \]
\[ = A'B'A'\]
\[ = ABA \left[ \because A =\text{ A' and B} = B' \right]\]
\[Since \left ( ABA \right)' = ABA, ABA \text{ is a symmetric matrix} .\]
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