A matrix T (with entries, say, in the field \(\mathbf { C }\) of complex numbers) is diagonalizable if there exists a non-singular matrix S such that \(S T S ^ { - 1 }\) is diagonal. Prove that if \(a , \lambda \in \mathbf { C }\) with \(a \neq 0\) , then the following matrix is not diagonalizable:
\[ T = { \left( \begin{array} { l l l } { 1 } & { a } & { 0 } \\ { 0 } & { 1 } & { a } \\ { 0 } & { 0 } & { \lambda } \end{array} \right) } \]