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
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
4 views
1 Answers
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.
4 views
Answered