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## Homework Statement

I need to prove that a 4x4 matrix has 2 zero eignenvalues.

**2. The attempt at a solution**

I have tried to obtain the characteristic equation but calculating the determinant of a relevant 4x4 is rather daunting as there aren't many zeros.

I was wondering if there is any other way to prove the statement without resorting to this brute force approach.

Thank you in advance!