Matrix/44/Depending on k/Invers to itself/Exercise

Prove that the matrix

${\begin{pmatrix}0&0&k+2&k+1\\0&0&k+1&k\\-k&k+1&0&0\\k+1&-(k+2)&0&0\end{pmatrix}}$

for all ${}k$ is the inverse of itself.

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