2 The elements of a group \(G\) are the complex numbers \(a + b \mathrm { i }\) where \(a , b \in \{ 0,1,2,3,4 \}\). These elements are combined under the operation of addition modulo 5 .
- State the identity element and the order of \(G\).
- Write down the inverse of \(2 + 4 \mathrm { i }\).
- Show that every non-zero element of \(G\) has order 5 .