Determinant problem

Subject classification: this is a mathematics resource.

Type classification: this is a quiz resource.

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,

$\Delta ={\begin{vmatrix}m&-1&-1&\dots &-1\\-1&m&-1&\dots &-1\\-1&-1&m&\dots &-1\\\vdots &\vdots &\vdots &\ddots &\vdots \\-1&-1&-1&\dots &m\end{vmatrix}}$

What is $\Delta$ as a function of $m$?

Solution.