Cracking GRE Sub第四版抽代问题

严小周UID: 2237598

P255
13. Let G be the group generated by the elements x and y and subject to the following ralations:
x^2=y^3,y^6=1, and x^(-1)yx=y^(-1）.  Express in simplest form the inverse of the element z=x^(-2)yx^3y^3.

答案是yx

有同学可以指导一下解法吗？

treemantanUID: 2770681

z=x^(-1)*(x^(-1)y*x)x^2y^3(结合律)
=x^(-1)y^(-1)y^3*y^3(under relations)
=(yx)^(-1)y^6
=(yx)^(-1)
therefore, the answer is yx