Using $\det(A-\lambda{}I)=0$ Find the eigenvalues for the given matrix: $ A=\begin{bmatrix} 1&-1&0&0\\ 3&5&0&0\\ 0&0&1&5\\ 0&0&-1&1\\ \end{bmatrix} $
The patterns in this matrix are obvious, so I am assuming there is a way to simplify this problem without expanding by a row/column, which could become messy really fast (although the abundance of zeros should help.) I just need a little direction.