Diagonalizable matrix with only one eigenvalue I have a question from a test I solved (without that question.. =) 
"If a matrix $A$ s.t $A$ is in $M(\mathbb{C})$ have only $1$ eigenvalue than $A$ is a diagonalizable matrix"
That is a false assumption since a ($n\times n$ matrix) a square matrix needs to have at least $n$ different eigenvalues (to make eigenvectors from) - but doesn't the identity matrix have only $1$ eigenvalue?...

It's pretty simple to see that:
A diagonalizable matrix  has a unique eigenvalue if and only if it's a scalar matrix.
