For the infinite group of non-zero complex numbers under multiplication, state the identity element and the inverse of \(1 + 2 \mathrm { i }\), giving your answers in the form \(a + \mathrm { i } b\).
For the group of matrices of the form \(\left( \begin{array} { l l } a & 0 0 & 0 \end{array} \right)\) under matrix addition, where \(a \in \mathbb { R }\), state the identity element and the inverse of \(\left( \begin{array} { l l } 3 & 0 0 & 0 \end{array} \right)\).