Countless solutions a=2
The unique solution A is not equal to 2, and A is not equal to 0.
Solution process
When a(a-2)=0 and 4(a-2) is not equal to 0, there is no solution, so find a=0.
When a(a-2)=0 and 4(a-2)=0, there are countless solutions, so a=2 is found.
When a(a-2) is not 0 and 4(a-2) is not 0, the unique solution A is not equal to 2 and A is not equal to 0.