If A is similar to B then $A^2$ is similar to $B^2$ im not sure how to begin to prove this, all i know is that for two matrices to be similar, the following equation must be true
$A = PBP^{-1}$
any help will be appreciated

The definition of $A \sim B$ is that there exists an invertible matrix $P$ of the same dimensions as $A$ and $B$ that satisfies $A = PBP^{-1}$.
You just need to show that:
$$A^{2} = AA = (PBP^{-1})(PBP^{-1}) = PB(P^{-1}P)BP^{-1} = PBIBP^{-1} = PBBP^{-1} = PB^{2}P^{-1}$$
And then conclude that, in fact, there exists an invertible matrix $P$ such that 
$$A^{2} = PB^{2}P^{-1}\Rightarrow A^{2} \sim B^{2}$$
And you're done.
