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

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SUMMARY

The discussion focuses on proving that the order of elements x and y in a group G is equal to 4, given the equations x-1yx = y-1xy. By substituting x-1 in the first equation with the left-hand side of the second equation, the conclusion y2x2 = 1 is derived. Further manipulation leads to the result y2 = x2, confirming that both elements share the same order.

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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
 
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Please help me....
 
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.
 

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