Answer
See solution for one example
Work Step by Step
$\begin{bmatrix}
1&0\\1&1
\end{bmatrix}$. The matrix is invertible, with inverse$\begin{bmatrix}
1&0\\-1&1
\end{bmatrix}$ but it is not diagonalizable because it has one eigenvalue, 1 with an eigenspace of dimension 1.
Note it can be any triangular 3 by 3 matrix with 3 nonzero values and equal values on its main diagonal.
