If A and B are matrices of the same order, then AB^T − BA^T is a

(a) skew-symmetric matrix
(b) null matrix
(c) unit matrix
(d) symmetric matrix

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Solution

(AB^T − BA^T)^T = (AB^T)^T − (BA^T)^T
= BA^T − AB^T
= −(AB^T− BA^T)

Therefore, AB^T − BA^T is a skew-symmetric matrix.

Hence, the correct option is (a).

Disclaimer: There is a misprint in the question. It should be BA^Tinstead of B^TA.

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