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Q.
If $A$ is symmetric as well as skew-symmetric matrix, then $A$ is
Matrices
Solution:
Let $A =\left[ a _{ ij }\right]_{ n \times m } .$ Since $A$ is skew-symmetric $a _{ ii }=0$
$( i =1,2, \ldots \ldots, n )$ and $a _{ ji }=- a _{ ji }( i \neq j )$
Also, $A$ is symmetric so $a_{j i}=a_{j i} \forall i$ 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