In each of the following parts, either give an example of a linear function T: C$^2$ -> C$^2$ with the specified properties (and show that your example has the desired properties), or prove that no example exists. 

(a) Diagonalizable and invertible.
(b) Not diagonalizable and not invertible.
(c) Diagonalizable, but not invertible.
(d) Invertible, but not diagonalizable.

For (c) the matrix $\begin{bmatrix}0 & 0\\0 & 0\end{bmatrix}$is an example
and for (d) the matrix $\begin{bmatrix}1 & 1\\0 & 1\end{bmatrix}$is an example, but how do I get functions that give these matrices? For (a) and (b) I'm not sure of a matrix.