How to prove the order of x,y in this case

[ranoo]

If x^-1yx=y^-1 and y^-1xy=x^-1 for the elements x,y of a group G , show that the order of x equal the order of y equal 4

 

[ranoo]

Please help me....

 

[Wizlem]

Replace x^-1 in the equation on the left with the left hand side of the equation on the right and you can get y²x²=1. Multiply the left hand side of the equation on the right by the right hand side of the equation on left and vice versa and you'll get y²=x².