Question

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

• A. Diagonal
• B. null zero matrix
• C. Triangular
• D. None of these

Answer 1

Answer: (B)

Let $A={\left[a_{ij}\right]}_{n\times m}.$ Since $A$ is skew-symmetric $a_{ii}=0$
$(i=1,2,\dots \dots ,n)$ and $a_{ji}=-a_{ji}(i\ne j)$
Also, $A$ is symmetric so $a_{ji}=a_{ji}\forall i$ and $j$
$\therefore a_{ji}=0\forall i\ne j$
Hence $a_{ij}=0\forall i$ and $j\Rightarrow A$ is a null zero matrix