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If A and B are symmetric matrices, prove...

If A and B are symmetric matrices, prove that AB BA is a skew symmetric matrix.

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The correct Answer is:
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`: ' `A and B are symmetric matrices .
`therefore A' =A and B'=B.. .(1)`
`Now ,(AB-Ba)'=(Ab)'-(BA)]=B'A'-A'B'`
`=BA-AB ` from equation(1)
`=- (AB-BA )`
`therefore `AB-BA is skew symmetric matrix.
hence proved .
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