# If matrix A is invertible, is it diagonalizable as well?

If a matrix A is invertible, then it is diagonalizable. Is it true or false?

• True if $A$ is $1\times 1$. Dec 12 '13 at 18:17

It is false. Consider $\begin{pmatrix} 1 & 1 \\ 0 & 1\end{pmatrix}$