Question

IF $A$ be a square matrix, then $A+A^T$ is a symmetric matrix ?

• A. True
• B. False

Answer 1

The correct option is A True

Given:$A$ is a square matrix

and $A$ is said to be symmetric if $A=A^T$

$\Rightarrow {(A+A^T)}^T=A^T+{\left(A^T\right)}^T$

$=A^T+A$

$=A+A^T$

Hence proved.