Australia's Prime Minister Julia Gillard has been sworn in on Tuesday and is now faced with the challenge of holding together a precarious coalition government after cliffhanger elections. The ceremony caps weeks of drama after the party revolt against former leader Kevin Rudd, followed by polls that produced the first hung parliament in decades and left Gillard relying on Greens and independent MPs for support. Gillard's first cabinet as an elected leader contains potential divisions with Rudd sitting alongside the party powerbrokers credited with orchestrating the sudden and surprising Labor mutiny in June. The prime minister was forced into a late change just hours before the ceremony by announcing a minister for Aboriginal health, following strong complaints when the post was left out of the original line-up.