Question

Let A and B both be $3\times 3$ matrices. Then, ${(AB)}^T=BA,$ if

• A. A is skew-symmetric and B is symmetric
• B. B is skew-symmetric and A is symmetric
• C. A and B are skew-symmetric
• D. None of the above

Answer 1

Answer: (C)

Let A and B are skew-symmetric.
$\Rightarrow$ $A^T=-A$ and $B^T=-B$ ..(i)
Given, ${(AB)}^T=B^T{A}^T$
$=(-B)(-A)$ [from Eq. (i)] $=BA$