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

Let $A = {[a_{ij}]}_{n \times m}$ Since A is skew–symmetric $a_{ii} = 0$

$(i = 1, 2, \dots \dots, n) and a_{ji} = - a_{ji} (i \neq j)$

Also, A is symmetric so $a_{ji} = a_{ji} \forall i and j$

$∴ a_{j i} = 0 \forall i \neq j$

Hence $a_{ij} = 0 \forall i and j \Rightarrow A$ is a null zero matrix.

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