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

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

Text Solution

Verified by Experts

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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