Another old idea:

### 2011-02-03

Given a matrix ,

Prove this and extend it to general matrices. Can you go further than that?

### Suggestions

- For matrices, use the Laplace Expansion (which was probably how you learned to calculate determinants in school, anyway).
- Derive a general formula for matrices using Mathematical Induction.
- Determinants for non-square matrices?
- Are there consequences for the eigenvalues?

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