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Transpose Conjugate

If A and B ar...

Question

If A and B are symmetric matrices of same order and X= AB + BA and Y = AB – BA, then $(X Y)^{T}$ is equal to

A

XY

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B

YX

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C

– YX

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D

None of these

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Solution

The correct option is C – YX
$X = A B + B A \Rightarrow X^{T} = X$
$a n d Y = A B - B A \Rightarrow Y^{T} = - Y$
$N o w, (X Y)^{T} = Y^{T} \times X^{T} = - Y X$

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