Question

If $A$ is a square matrix, then

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

Answer 1

Answer: (A)

$A+A^T$ is symmetric

Now, ${(A+A^T)}^T=A^T+{\left(A^T\right)}^T$
$=A^T+A$
$\therefore A+A^T$ is symmetric matrix.