# Multiple eigenvalues - any hints would be appreciated

## 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.

I assume you mean that you have a specific 4 by 4 matrix that you have not shown us. No, there is no 'simple' way to calculate eigenvalues except for special matrices. Whether or not there exist a special trick for your matrix, we cannot say because you do not show us the matrix. Just calculate the determinant of $A- \lambda I$ and set it equal to 0. With a f4 by 4 matrix that will give you a fourth degree polynomial equation.