[tex] \it X = \begin{pmatrix} a\ \ \ \ \ b
\\ \\
c\ \ \ \ \ d \end{pmatrix} \Rightarrow X^t = \begin{pmatrix} a\ \ \ \ \ c
\\ \\
b\ \ \ \ \ d \end{pmatrix} \Rightarrow -X^t = \begin{pmatrix} -a\ \ \ \ \ -c
\\ \\
-b\ \ \ \ \ -d \end{pmatrix}
\\ \\ \\
X= X^t \Rightarrow \begin{cases} \it a=-a \Rightarrow a = 0
\\ \\
\it d=-d \Rightarrow d = 0
\\ \\
c=-b \in \mathbb{R}\end{cases} [/tex]
[tex] \it X\in {Q} \Rightarrow X = \begin{pmatrix} 0\ \ \ \ \ b
\\ \\
-b\ \ \ \ \ 0 \end{pmatrix} \Rightarrow det(X) = b^2 \geq 0 [/tex]
