If A is symmetric matrix, then B AB is…………

If A is a symmetric matrix, then B AB is a symmetric metrix. = = (AB) ( B ) = B A B = Therefore, B AB is a symmetric matrix.

Matrices — Class 12 Maths Solution

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Question

If A is symmetric matrix, then ${B^\prime }AB$ is…………

Step-by-step Solution

If A is a symmetric matrix, then ${B^\prime }AB$ is a symmetric metrix.

${\left[ {{B^\prime }AB} \right]^\prime } = {\left[ {{B^\prime }(AB)} \right]^\prime }$

$= {(AB)^\prime }{\left( {{B^\prime }} \right)^\prime }$

$= {B^\prime }{A^\prime }B$
$= \left[ {{B^\prime }{A^\prime }B} \right]$

Therefore, ${B^\prime }AB$ is a symmetric matrix.

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Matrices. Curated by Sachin Sharma. Free for all students.