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Question
If A and B are symmetric matrices, then BA – 2AB is a ______.
Solution
If A and B are symmetric matrices, then BA – 2AB is a neither a symmetric nor a skew-symmetric matrix.
Explanation:
Let Q = (BA – 2AB)
Q' = (BA – 2AB)'
= (BA)' – (2AB)'
= A'B' – 2(AB)' .....[∵ (kA)' = kA']
= A'B' – 2B'A'
= AB – 2BA .....[∵ A' = A an B' = B]
= –(2BA – AB)
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