A:

Set a = {a 2- 1, a-2, a}, set B={3, 2a- 1, a 2}

A∩B={3}

Obviously, there must be an element in set A that is 3.

1)

A- 1 = 3, the solution is: a=-2 or a=2.

A=-2, A={3, -4, -2}, B={3, -5, 4}, which is consistent.

A=2, A = {3,0,2}, B = {3,3,4}, according to the anisotropy of elements, it does not conform.

2)

A-2=3, a=5, A = {24,3,5}, B = {3,5,9}, which do not match.

3)

A=3, A = {8, 1, 3}, B = {3 3,5,9}, which is consistent.

To sum up, a=-2 or a=3.