The question:

Prove that if A ~ B then B ~ A

My attempt:

1.$\displaystyle A = S^{-1}BS$

2. $\displaystyle B = S^{-1}AS$

Sub 1 into 2:

$\displaystyle A = S^{-1}(S^{-1}AS)S$

Let S = I

Thus A = A, and similarly B = B. Which is true. I'm pretty sure this isn't the correct process. What should I be doing to prove this? Thanks.