The product of the non-zero eigenvalues of the matrix is \_\_\_\_.
$$\pmatrix{1&0&0&0&1\\0&1&1&1&0\\0&1&1&1&0\\0&1&1&1&0\\1&0&0&0&1}$$

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### My attempt:

Well, answer is $6$. It's a big matrix (but not more), so finding eigenvalues by characteristics equation will be lengthy process. I'm trying for any short trick to find eigenvalues of a big $n \times n$ matrix.

This explained "[eigenvalues by inspection](https://math.stackexchange.com/questions/152796/eigenvalues-by-inspection)". I'm not getting properly.

> 
> Can you explain, eigenvalues and eigenvectors by inspection for this matrix in steps please?
> 
> 
> 

Can you explain in steps.