Hi! Please help me with question 7.

Thank you so much!

7. Prove that the arbitrage free initial price for an American call option is the same as the arbitrage free initial price for a European call option. Furthermore, show that with this initial (arbitrage free) price, if the buyer of an American call option waits until the expiration date to exercise the option, this prevents the seller from making a risk free profit (that is, it prevents a seller's arbitrage)