Explanation: If matrix $A$ is symmetric$A^{T}=A$If matrix $A$ is skew-symmetric$A^{T}=-A$Also, diagonal elements are zero. Since, it is given that matrix $A$ is both symmetric and skew-symmetric.$\therefore \; \; A=A^{T}=-A$Which is only possible if $A$ is zero matrix.$A=\begin{bmatrix}0 & 0 \\ 0 & 0\end{bmatrix}=A^{T}=-A$Thus, if a matrix A is both symmetric and skew symmetric, then $A$ is necessarily a zero matrix.