If matrix is diagonalizable, eigenvalue? 
Let $A$ be an $n \times n$ matrix and suppose $A$ is diagonalizable and the only eigenvalue is $\lambda = k$, what can you say about matrix $D$ where $A = P^{-1} D P$, for invertible matrix $P$.

So if the only eigenvalue of $A$ is $\lambda = k$, what can I say about $D$? 
I know that $D$ is a diagonal matrix, but is it necessarily true that $D = \text{diag } (k, k, ... , k)$ ?

The first question is: What can you say about $A$?
You know it's diagonalizable, so write it out in a diagonal form.
You know the only possible eigenvalue, so you know the diagonal entries.
What does it look like?
Notice that $A$ was not assumed to be diagonal, just diagonalizable.
What happens to it after you change the basis?
Once you have found $A$, you can find $D$ easily.
