Question

If a matrix $A$ is both symmetric and skew symmetric, then

• A. $A$ is a diagonal matrix
• B. $A$ is a zero matrix
• C. $A$ is a scalar matrix
• D. $A$ is a square matrix

Answer 1

The correct option is B $A$ is a zero matrix

Given that $A$ is a symmetric and skew symmetric matrix,
$\Rightarrow a_{ij}=a_{ji}$ and $a_{ij}=-a_{ji}$
$\Rightarrow a_{ij}=0$
$A$ is a zero matrix