[Math] Does interior of closure of open set equal the set

Question

Would you help me to solve this question. Is it true that if A is open set then $A=\operatorname{int}(Cl(A))$ where Cl(A) denote the closure of A. I already prove that $A\subseteq\operatorname{int}(Cl(A)) $ only using definition of closure and interior, but have no idea about proving $\operatorname{int}(Cl(A))\subseteq A$ or give a counter example.

Answer 1

HINT: See what happens with $A=(0,1)\cup(1,2)$.