Fill in the blank. If A is symmetric matrix, then B′AB is _______… - Vidyadip

Question

Fill in the blank.
If A is symmetric matrix, then B′AB is _________.

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Answer

If A is symmetric matrix, then B′AB is symmetric matrix.Solution:
Given A is symmetric matrix
$\therefore$ A' = A Now [B'AB]' = [B'(AB)]' = (AB)'(B')' $[\because$ (AB)' = B'A'$]$ = B'A'B = [B'AB] $[\because$ A' = A$]$ So, B'AB is a symmetric matrix.

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