You can prove \\((xx)^{-1}= x^{-1}x^{-1}\\) in a group, its a consequence of canceling and asocitivity.\\[(xy)(y^{-1}x^{-1})= x(yy^{-1})x^{-1}=xx^{-1}=1\\]

Then let y = x. Man it's been a long time since I've used that.