What are the eigenvectors of 4 times the identity matrix? What are the eigenvectors of the identity matrix
$
 I=
  \left[ {\begin{array}{cc}
   1 & 0 & 0 \\       0 & 1 & 0 \\    0 & 0 & 1 \\  \end{array} } \right]
$

Follow the definition. In order to determine the eigenvectors of a matrix, you must first determine the eigenvalues. 
Substitute one eigenvalue λ into the equation Ax = λx or, equivalently, into (A − λI)x = 0 and solve for x; the resulting nonzero solutions form the set of eigenvectors of A corresponding to the selected eigenvalue. This process is then repeated for each of the remaining eigenvalues.
