I will denote x-inverse as x' and the identity as e.

I'm asked to solve the two equations below simultaneously:

(1) ax^2 = b and (2) x^3 = e

Here's what i did:

ax^3 = bx (by multiplying (1) on the right by x)

Now, ae = bx (since x^3 = e)

b'a = x (by multiplying b' on the left)

BUT, if we plug in the above x into (1) we get a(b'a)(b'a) = b which isn't true..????

I've tried manipulating both (1) and (2) in many different ways but always come up with x = b'a.

What have I done wrong? Can someone show how to do this correctly please. Thanks a lot!