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Given $n\in \mathbb N$, how can I compute the determinant of $(a_{ij})_{1\leq i,j \leq n} \in \mathcal M_{n\times n}(\mathbb R)$ where, for each $1\leq i,j\leq n:$ $$a_{ij}= \begin{cases} \lambda &i=j \\ \mu & i\neq j \end{cases}$$
The only (or the only easy) way to do this I think involves using...
