Finding the rank of an non-invertible matrix I have a $3\times3$ matrix with three different eigenvalues $0,1, 2$. 
The question is: what is the rank of this matrix? If the matrix was invertible, I could say that the rank was equal to $n=3$. But as zero is an eigenvalue of this matrix, this matrix does not satisfy the Invertible Matrix Theorem. 
How should I determine the rank? Thanks in advance. 

In a simplistic sense, for a square matrix-
Rank = Number of non-zero eigen-values
