The matrix $A =\begin{bmatrix}i &1-2i\\-1-2i&0\end{bmatrix}$ is which of the following?
Answer & explanation
Correct answer: option 4
The correct answer is Option 4: skew-hermitian
We have,
$\bar A =\begin{bmatrix}i &1+2i\\-1+2i&0\end{bmatrix}$
$(\bar A)^T =\begin{bmatrix}-i &-1+2i\\1+2i&0\end{bmatrix}=-\begin{bmatrix}i &1-2i\\-1-2i&0\end{bmatrix}=-A$
Hence, A is skew-hermitian.