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)

null zero matrix

Answer 2

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