Question

If $A$ is symmetric as well as skew-symmetric matrix, then $A$ is

• A. diagonal matrix
• B. null matrix
• C. triangular matrix
• D. none of these

Answer 1

The correct option is B null matrix

Since, A is skew-symmetric.
$A^T=-A$
Since, A is symmetric.
$A^T=A$
$\Rightarrow -A=A$
$\Rightarrow 2A=O$
$\Rightarrow A=O$
Hence, A is a null matrix.