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Suppose i have list equations like below {x(a-1)==0,x y (a-1)==0,x^2(a-1)==0} Which x and y are arbitrary variable with arbitrary power change every time and unknown variable is a . I use reduce but it solve equations for one conditional expression which is below x==0 & y==0 & a=1 How can solve problem in general?

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SolveAlways[{x (a - 1) == 0, x y (a - 1) == 0, x^2 (a - 1) == 0}, {x, y}]
(* {{a -> 1}} *)
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