Suppose we have a $10 \times 10$ matrix $A$ which has $0$'s on the main diagonal (so that the trace of $A$ is $0$). Also suppose that $A^2=I$. How can we find a determinant of $A+2I$?
Based on my previous question, I tried to find eigenvalues, as in find $\lambda$ so that $A-\lambda I$ is not invertible. I have trouble again doing this, given the hypotheses here that are different than those of my previous question. How can I proceed in finding eigenvalues so I can construct a spectrum and find the determinant?