Let N be a 3 by 3 matrix with real number entries. The matrix N is such that N2 = 0. The eigen values of N are A. 0, 0, 0 B. 0, 0, 1 C. 0, 1, 1 D. 1, 1, 1

The correct answer is $\boxed{\text{A}. 0, 0, 0}$.

An eigenvalue of a matrix $A$ is a number $\lambda$ such that there exists a nonzero vector $v$ such that $Av = \lambda v$. The vector $v$ is called an eigenvector of $A$ corresponding to the eigenvalue $\lambda$.

If $N^2 = 0$, then $N$ is a nilpotent matrix. A nilpotent matrix is a matrix such that $N^k = 0$ for some positive integer $k$. It is known that the eigenvalues of a nilpotent matrix are all zero.

Therefore, the eigenvalues of $N$ are all zero.