We throw a die twice. Give a suitable sample space for this experiment and then identify the elements each of the following events contains:

A1: the outcome of the first throw is 6;

A2: the outcome of the second throw is a multiple of 3;

A3: the outcome of the first throw is 6 and the outcome of the second throw is a multiple of 3;

A4: the sum of the two outcomes is 7;

A5: the sum of the two outcomes is at least 9;

A6: the two outcomes are identical.