To find the order of element b, we need to find the smallest positive integer n such that b^n = e, where e is the identity element of the group G.

Given that aba^(-1) = b^2, we can manipulate this equation to obtain a^2ba^(-2) = b^2.

Let's consider the expression a^2ba^(-2). We know that o(a) = 3, which means a^3 = e (the identity element). Therefore, we can rewrite a^2ba^(-2) as a^3ba^(-3).

Now, let's multiply both sides of the equation a^3ba^(-3) = b^2 by a to obtain a^4ba^(-3) = ab^2.

Since a^3 = e, we can simplify the equation further to obtain aba^(-3) = ab^2.

Next, we can multiply both sides of the equation aba^(-3) = ab^2 by a^3 to obtain a^4ba^(-3) = a^4b^2.

Since a^3 = e, we can simplify the equation further to obtain aba = a^4b^2.

Now, let's multiply both sides of the equation aba = a^4b^2 by b to obtain abab = a^4b^3.

Since b is not the identity element, we can cancel b from both sides of the equation to obtain aba = a^4b^2.

We can rewrite this equation as a^(-1)aba = a^3b^2.

Since o(a) = 3, we know that a^3 = e. Therefore, we can simplify the equation further to obtain a^(-1)aba = eb^2.

Finally, we can cancel a from both sides of the equation to obtain ba = eb^2.

Since eb^2 = b^2, we have ba = b^2.

Now, let's consider the equation ba = b^2. We can rewrite this equation as ba = b*b.

If we multiply both sides of the equation ba = b*b by b^(-1), we obtain bab^(-1) = b.

Since aba^(-1) = b^2, we know that bab^(-1) = b^2.

Therefore, we have b^2 = b, which means b is idempotent.

Since b is not the identity element, the order of b cannot be 1.

To find the order of b, we can consider the powers of b: b, b^2, b^3, ...

If we continue to raise b to higher powers, we will eventually reach a power n such that b^n = e, where e is the identity element.

Therefore, the order of b is the smallest positive integer n such that b^n = e.

By examining the equation b^2 = b, we can see that b^2 = b*b = b.

Therefore, b^2 = b implies that b^3 = b^2*b = b*b*b = b^2 = b.

Similarly, b^4 = b^3*b = b*b = b^2 = b.

We can continue this pattern and observe that b^n = b for all positive integers n.

Therefore, the order of b is