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If $A$ is a symmetric matrix, then matrix $M^{\prime} A M$ is
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Symmetric
$\left(M^{\prime} A M\right)^{\prime}=M^{\prime} A^{\prime} M=M^{\prime} A M$
$\{A$ is symmetric. Hence $M^{\prime} A M$ is a symmetric matrix).
$\{A$ is symmetric. Hence $M^{\prime} A M$ is a symmetric matrix).
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