= Solution
Let $A_1,A_2,A_3$ denote the three matrices in their printed order. A <Hermitian matrix> satisfies $A^\dagger=A$, a <unitary matrix> satisfies $A^\dagger A=I$, and an <orthogonal matrix> is real with $A^TA=I$.
For the first matrix, $A_1^\dagger=A_1$ and $A_1^2=I$. It is therefore \b[Hermitian and unitary]. It is not real, and even allowing complex entries in the transpose test gives $A_1^TA_1=-I$, so it is not orthogonal.
The second matrix is $A_2=iI$. Thus $A_2^\dagger A_2=(-iI)(iI)=I$, whereas $A_2^\dagger=-A_2$ and $A_2^TA_2=-I$. It is \b[unitary only] among the listed classes.
The third matrix is real, but direct multiplication gives
$$
A_3^TA_3=\operatorname{diag}\left(1,\frac14,1\right).
$$
It is neither orthogonal nor unitary. Its unequal off-diagonal transpose entries also show $A_3^T\ne A_3$, so it is \b[none of the three]. The common prefactor $1/2$ applies to the central diagonal entry as well; replacing that entry by one would describe a different matrix.
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