I'm having a bit of trouble understanding this exercise: Indicate whether the following grammar describes a regular language. Prove your answer.
G4: $S \to aS|aSbS|ε$
My answer is using this regular expression: $L= \{a,ab\}^*$ therefore, the grammar describes a regular language; The official solution says: Not regular. Use the pumping lemma and the string $(a^p)(b^p)$ and pump down. (where ^ means to the power of)
Can you help me understand why my regular expression doesn't work or why the pumping lemma proves the language is not regular?