Here was one of the most powerful women in world finance, deftly answering questions ranging from educating girls to concerns about China's shadow banking sector.

Her polished performance, which drew a stream of compliments on Twitter, was no surprise for those who have followed the career of the talented Frenchwoman, whose flawless English reflects her partial education in the United States.

In Sydney for the G20 - the meeting of finance ministers and central bankers from the world's most powerful economies -  Lagarde is no stranger to the spotlight. She was the first women to head up an international law firm and the first female finance minister of a developed country.

She smashed through another glass ceiling when, in mid-2011, she became the head of the International Monetary Fund, the powerful body which puts stabilisers on the world's financial system.

Like Lagarde, the petite but intellectually imposing Yellen is also a trailblazer in a world still heavily dominated by men. Last month, the snowy haired public servant and academic became the first woman to chair the century-old US Federal Reserve, the world's most influential central bank.

As prominent economist Meghnad Desai, a former colleague of Yellen's, noted recently to The Washington Post, it is a world where "a woman has to persist and prove more than once that shes as good as anybody else".

"I never thought that the world would finally recognise and reward her the way that it has. She has punched her way to the top by sheer ability."

While Lagarde has used her role at IMF to speak out about the role of women in public life, Yellen has studiously shied away from gender-related issues. The 67-year-old also reportedly told Fed staff to refer to her position as "chair" rather than "chairwoman".

In contrast, Lagarde has said publicly that women would be better leaders in crisis situations.

"My favourite example is Iceland," Lagarde told Harvard Business Review last year.

"The country essentially went down the tubes. Who was elected prime minister? A woman. Who was called in to restore the situation with the banks? Women. The only financial institution that survived the crisis was led by a woman."

On Thursday, she told the Q&A audience to a round of applause that education for girls "is an absolute must".

"I believe that society, including communities and also families, should actually do everything they can to help young girls [and] women to carry out some of the duties we have ... and make those compatible with professional life, if it is the desire of those young girls and women.

"From my personal experience, you don't necessarily succeed on all fronts at the same time.

"So you should try to be yourself, do your best, and have as much confidence as you can in what you do, and not hesitate to call for help from other women, from other men, from family members, from husband, companion, however, because it's a joint operation. It's not flying solo."