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Question
If A and B are symmetric matrices of the same order, then (AB′ –BA′) is a ______.
Options
Skew symmetric matrix
Null matrix
Symmetric matrix
None of these
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Solution
If A and B are symmetric matrices of the same order, then (AB′ –BA′) is a skew-symmetric matrix.
Explanation:
(AB′ –BA′)′ = (AB′)′ – (BA′)′
= (BA′ – AB′)
= – (AB′ –BA′)
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