Determinant/Laplace-matrix/Complete graph/Exercise

We consider the matrix

${\begin{pmatrix}2&-1&-1\\-1&2&-1\\-1&-1&2\end{pmatrix}}.$

1. Compute the determinant of ${}M$.
2. Determine the determinant for every matrix that arises when we remove from ${}M$ a row and a column.

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