Question:
If $A$ and $B$ are matrices of the same order, then $A B^{T}-B A^{T}$ is a
(a) skew-symmetric matrix
(b) : matrix
(c) unit matrix
(d) symmetric matrix
Solution:
$\left(A B^{T}-B A^{T}\right)^{T}=\left(A B^{T}\right)^{T}-\left(B A^{T}\right)^{T}$
$=B A^{T}-A B^{T}$
$=-\left(A B^{T}-B A^{T}\right)$
Therefore, $A B^{T}-B A^{\top}$ is a skew-symmetric matrix.
Hence, the correct option is (a).
Disclaimer: There is a misprint in the question. It should be $B A^{\top}$ instead of $B^{\top} A$.
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