(a) That's wrong. It is true that the powers of the Crown are very largely exercised following the advice following the advice of the government of the day. For example, the government advises the Crown about who to appoint as judges.

But the Crown, which historically enjoyed a complete and unrestricted power to rule, is considered to retain any powers that have not been taken away by constitutional changes. These remaining powers are referred to as the Crown's 'reserve' powers. They are exercised at the discretion of the Crown, regardless of what the government of the day might wish.

The powers exercised by the Crown mean that the Crown does not play a purely ceremonial or symbolic role in Australian government.