Question

If $A$ is any square matrix, then which of the following is skew-symmetric?

• A. $A+A^T$
• B. $A-A^T$
• C. $A{A}^T$
• D. $A^{T}A$

Answer 1

Answer: (B)

$(A-A^T{)}^T=A^T-(A^T{)}^T=A^T-A=-(A-A^T)$
Hence, $(A-A^T)$ is skew-symmetric.