# Question about Lie algebra, where am I going wrong?

Let $M:= \begin{pmatrix}1 & 2 & 3 & 4\\3 & 4 & 4 & 1\\1 & 9 & -1 & -3\\9 &5 & -2 & -4\end{pmatrix} = \begin{pmatrix} A & B\\C & -A^{t}\end{pmatrix}$ and $J:=\begin{pmatrix} &&&1\\&&1&\\&-1&&\\-1&&&\end{pmatrix}$. By how $M$ is defined, $M$ belongs to $\mathfrak{sp}_{4}$. But $M^{t}J + JM \neq 0$. Where is my error?

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$J$ should be $\begin{pmatrix}&I\\-I&\end{pmatrix}$.