Question

Let A be a square matrix. Which of the following is/are not symmetric matrix/matrices?

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

Answer 1

Answer: (C)

$A-A^T$

We know a square matrix $A$ is called symmetric if $A^T=A$
. Let $P=A-A^T\Rightarrow P^T=(A-A^T{)}^T=A^T-A=-P\Rightarrow$ This is not a symmetric matrix, it is skew symmetric matrix.
All other matrices in the other option are symmetric.