If A and B are matrices of the same order,


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


$\left(A B^{T}-B A^{T}\right)^{T}=\left(A B^{T}\right)^{T}-\left(B A^{T}\right)^{T}$

$=B A^{T}-A B^{T}$

$=-\left(A B^{T}-B A^{T}\right)$

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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