The correct answer to this open question is the following.
Although there are no options attached or further context or references, we can say the following.
The two major social institutions in Australian society are the family and the government of Australia.
In the case of the family, it is a social institution in Australia that is the foundation and the pillar of Australian society. The family takes care of children and educates them in the family environment. Through family, Australian people inherit culture, traditions, and belief systems.
On the other hand, the government of Australia impact family and the community in that the government has the obligation of protecting society from any internal risks or international threats. The government has to create the proper conditions for Australian citizens to thrive. We are talking about the economic conditions and social peace so people can work and invest their money in Australia. In the cases needed, it has to regulate the economy and maintain political stability. The government has to create laws and legislation to maintain the social order, protecting the constitutional rights of the citizens.