Question

If the 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 square matrix
• D. None of these

Answer 1

Answer: (B)

$A$ is a zero matrix

Answer 2

The correct answer is B:$A$ is a zero matrix
$A'=A\,\, and\,\, A'=-A$
$\implies A=-A$
$\implies A+A=0$
$\implies 2A=0$
$\implies A=0$
Therefore, $A$ is a zero matrix.