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Question
If A is symmetric matrix, then B′AB is ______.
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Solution
If A is symmetric matrix, then B′AB is a symmetric matrix.
Explanation:
If A is a symmetric matrix
∴ A' = A
Let P = B'AB
P' = (B'AB)'
= B'A'(B')' .....[∵ (AB)' = B'A']
= B'AB .....[∵ A' = A and (B')' = B]
∴ P' = P
So, P is a symmetric matrix
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