## Quiz 13 (Part 2) Find Eigenvalues and Eigenvectors of a Special Matrix

## Problem 386

Find all eigenvalues of the matrix

\[A=\begin{bmatrix}

0 & i & i & i \\

i &0 & i & i \\

i & i & 0 & i \\

i & i & i & 0

\end{bmatrix},\]
where $i=\sqrt{-1}$. For each eigenvalue of $A$, determine its algebraic multiplicity and geometric multiplicity.