Answer:
Let A is a matrix which is both symmetric as-well-as skew-symmetric matrix. \[\therefore \] \[A'=A\] ?(i) And \[A'=-\,A\] ?(ii) On comparing Eqs. (i) and (ii), we get \[A=-\,A\] \[\Rightarrow \] \[A+A=0\Rightarrow 2A=0\Rightarrow A=0\] Hence, matrix which is both symmetric as well as skew-symmetric is a null matrix.
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