Albert Barnes Commentary Esther 8:2

"And the king took off his ring, which he had taken from Haman, and gave it unto Mordecai. And Esther set Mordecai over the house of Haman." — Esther 8:2 (ASV)

His ring - that is the royal signet by which the decrees of the government were signed.

Over the house of Haman - Not only the building and the furniture, but the household – the vast train of attendants of all kinds that was attached to the residence of a Persian noble.