Determinant problem

Problem: Given a square, $m\times m$ matrix $M$ whose diagonal elements are each equal to $m$ and whose non-diagonal elements are each equal to $-1$, calculate its determinant.

In symbols,

$\mathrm{\Delta }=\left|\begin{array}{ccccc}m& -1& -1& \dots & -1\\ -1& m& -1& \dots & -1\\ -1& -1& m& \dots & -1\\ ⋮& ⋮& ⋮& \ddots & ⋮\\ -1& -1& -1& \dots & m\end{array}\right|$

What is $\mathrm{\Delta }$ as a function of $m$?

Solution.