Inverse matrix/Anti diagonal/Exercise

Determine the inverse matrix of

${\begin{pmatrix}0&0&\cdots &0&1\\0&0&\cdots &1&0\\\vdots &\vdots &1&\vdots &\vdots \\0&1&\cdots &0&0\\1&0&\cdots &0&0\end{pmatrix}}.$

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