class 12 maths matrices

If A and B are symmetric matrices of same order, then AB is symmetric if and only if..........

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📘 Matrices NCERT,Exemp,Q.no.80,Page 63 FillBlank

If A and B are symmetric matrices of same order, then AB is symmetric if and only if..........

Official Solution

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If A and B are symmetric matrices of same order, then AB is symmetric if and only if $AB = BA$.

$\therefore$ ${(AB)^\prime }$

$= {B^\prime }{A^\prime } = BA$
$= AB$

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