The matrix [ array cc 0 & -4+i 4+i & 0 array ] is

The given matrix A=\left[$\begin{array}{cc}0 & -4+\mathrm{i} \\ 4+\mathrm{i} & 0\end{array}$\right] Now, from options: From option (A): For Symmetric matrix $\mathrm{A}^{\mathrm{T}}=\mathrm{A}$ Now, A^{\mathrm{T}}=\left[$\begin{array}{cc}0 & 4+\mathrm{i} \\ -4+\mathrm{i} & 0\end{array}$\right] \neq \mathrm{A}\therefore \quad The given matrix is not symmetric $\therefore \quad$ option (A) is wrong. From option (B): For Skew-symmetric matrix $$\begin{aligned} & \mathrm{A}^{\mathrm{T}}=-\mathrm{A} \\ & =\left[\begin{array}{cc} 0 & 4+\mathrm{i} \\ -4+\mathrm{i} & 0 \end{array}\right] \neq-\mathrm{A} \end{aligned}$$\therefore \quad$Given matrix is not skew-symmetric$\therefore \quad$option (B) is wrong. From option (C): For Hermitian matrix$A^T=\bar{A}$, where$\bar{A}$is conjugate of matrix$A\bar{A}=\left[$$\begin{array}{cc}0 & -4-i \\ 4-\mathrm{i} & 0\end{array}$$\right] \neq \mathrm{A}^T\therefore \quad$option (C) is wrong. From option (D): For Skew-Hermitian matrix The diagonal element of a skew-hermitian matrix are pure imaginary or zero.$\mathrm{A}=\left[$$\begin{array}{cc} 0 & -4+\mathrm{i} \\ 4+\mathrm{i} & 0 \end{array}$$\right]$Here, diagonal element indicates that the given matrix is skew-hermitian matrix.$\therefore \quad$ option (D) is correct.