"If the Opposition won the majority in the Senate, would they sit on the right of the President?"

Thanks for your question.

As you know, at a federal election the party or coalition of parties with the support of the majority of members elected to the House of Representatives becomes the Australian Government. That team will sit to the right of the Speaker of the House of Representatives and to the right of the President of the Senate. So even if the opposition had a majority in the Senate they would still sit to the left of the President.

diagram to help explain If the Opposition won the majority in the Senate, would they sit on the right of the President?