Suppose that $\displaystyle {A}$ = $\displaystyle {\left(\begin{array}{cccc} {2}&-{1}&{0}&{0}\\-{1}&{2}&{0}&{0}\\{0}&{0}&-{2}&{2}\\{0}&{0}&{2}&-{2}\end{array}\right)}$. Find the sum of all the eigenvalues of $\displaystyle {A}$, i.e. the trace of $\displaystyle {A}$.

Trace of $\displaystyle {A}$ is Preview Question 6