Is the language $L=\{a^nb^n\} \cup \{aa*\}$ DCFL? Is the language $L=\{a^nb^n\} \cup \{aa*\}$ DCFL OR CFL?
The author says $L$ is CFL, but I am able to generate a Deterministic PDA for the corresponding language. I am naive in this subject and hence I am not sure whether its DCFL or CFL.

Can you provide an explanation that shows $L$ is either DCFL or CFL?

i dont know how to use math,i searched for the solution but didn't got any,my DPDA is shown in picture below.
Your PDA isn't deterministic, as it has moves for $q_0, \epsilon, a$ and $q_0, b, a$.