Conditional probability and Bayes rule

Question

I cannot understand why the following is not correct. I can understand the first line from the definition of conditional probability.
$P(A\cap B)=P(A|B)P(A) = \frac{P(B|A)P(A)}{P(B)}P(A)\text{, using Bayes rule where } P(A|B)=P(B|A)\frac{P(A)}{P(B)}$
And then rearranging to get $P(B)$ as
$P(B) = \frac{P(B|A)P(A)^2}{P(A\cap B)}$.

For context, I tried to solve a problem using this substituting in values for $P(A)$ and $P(B)$ but I got the wrong answer.

Answer 1

As noted in a comment, the error is in the first equality, which should be $P(A\cap B)=P(A\mid B)P(B)$ instead.