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If A and B are matrices of the same o...

If `A` and `B` are matrices of the same order, then `A B^T-B^T A` is a (a) skew-symmetric matrix (b) null matrix (c) unit matrix (d) symmetric matrix

Text Solution

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Let `P=(AB^(T)-BA^(T))`
`:. P^(T)=(AB^(T)-BA^(T))^(T)=(AB^(T))^(T)-(BA^(T))^(T)`
`=(B^(T))^(T) (A)^(T)-(A^(T))^(T)B^(T)=BA^(T)-AB^(T)`
`=-(AB^(T)-BA^(T))=-P`
Hence, `(AB^(T)-BA^(T))` is a skew-symmetric matric.
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Knowledge Check

  • If A and B symmetric matrices of the same order then AB-BA is a matrix which is

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    null
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    unit
    C
    symmetric
    D
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