Exercise
What are the invertible elements of Z/3Z × Z/3Z?
{(1,1), (2,2)}
{(1,2), (2,1)}
{(1,1), (1,2), (2,1), (2,2)}
No. Did you find out about (Z/3Z)*?
No. The unit element (1,1) is surely invertible.
Right!
Exercise
What are the invertible elements of Z/3Z × Z/3Z?
{(1,1), (2,2)}
{(1,2), (2,1)}
{(1,1), (1,2), (2,1), (2,2)}