Inside the house, Luciana and Antipholus of Syracuse are alone together. Luciana rebukes the man she believes to be her brother-in-law for not treating Adriana well; if he must betray his wife, she pleads, he should at least do it secretly. Antipholus S., meanwhile, insists that he is not Adriana's husband and then professes his love for Luciana. Appalled, she flees to find her sister.
Dromio of Syracuse joins his master and recounts how the kitchen maid, Nell, mistook him for her husband (who is, in fact, Dromio of Ephesus). Nell, as the Syracusan Dromio tells it, is a prodigiously fat, ugly, and fearsome woman, and he and his master have a good laugh at her expense. Then, Antipholus S. tells his slave that he intends to depart from Ephesus immediately and sends him to the harbor to book passage. Once Dromio is gone, his master ponders the beauty of Luciana but resolves not to be tempted to remain in the city, since "none but witches do inhabit here"(III, ii, 154). As he stands in thought, Angelo the goldsmith comes in and, mistaking him for Antipholus of Ephesus, gives him the gold chain that the Ephesian Antipholus had ordered, promising to stop by later to collect payment.
Angelo, we learn, is in debt to a Second Merchant, who threatens to arrest him unless the money is paid. The goldsmith promises to collect the sum from Antipholus of Ephesus, who he sees walking down the street with Dromio of Ephesus. Antipholus E. sends his slave off to buy rope, with which he plans to beat his wife and servants for locking him out of the house at the last meal. Next, he greets Angelo, who asks to be paid for his gold chain. Antipholus, of course, never received the chain, and refuses to pay, so Angelo has him arrested. At that moment, Dromio of Syracuse returns from the harbor, and mistaking Antipholus E. for his master, tells him which ships are ready to sail. Cursing, Antipholus orders him to be silent and sends him to Adriana to fetch a purse of money with which to pay his way out of jail.
Meanwhile, Luciana has told Adriana about how her "husband" declared his love for her and pledges her innocence of any illicit behavior. Adriana curses Antipholus furiously but admits to still feeling some love for him. Dromio of Syracuse dashes in to report that Antipholus has been arrested and needs money; Adriana sends Luciana to fetch it and then orders Dromio to hurry and save her husband from prison.
Her encounter with Antipholus of Syracuse provides an occasion for Luciana to expound again on her philosophy of marriage. She rebukes him for not being faithful and then says, "If you like elsewhere, do it by stealth; / Muffle your false love with some show of blindness (II.ii.7-8)." In other words, cheat if you must but at least pretend that you still love her, and don't get caught philandering. This assumption that men will have affairs, and that it is better not to know about them, fits in well with Luciana's world of docile women and dominating men, but it has unsettling implications in this case, since Antipholus is professing his love for her. By suggesting that her brother-in-law can commit adultery as long as he is not caught, one might argue, she implicitly suggests her own openness to his entreaties.
For his part, Antipholus' speech declaring his love for her has a touching desperation to it. The language, which promises his submission to her ("teach me, dear creature, how to think and speak [III.ii.33])," suggests a relationship that reverses Luciana's professed ideal of feminine obedience. In a sense, Antipholus seems to be using his infatuation to achieve what his search for his brother has not granted him--namely, a sense of self. "Transform me then," he entreats her, "and to your power I'll yield (III.ii.40)." If the enchantments of Ephesus threaten to strip him of his identity, then his love for Luciana offers it back to him through the re-creative powers of love.
I have written my own act wise summary of comedy of errors. Hope it will help students like me.