Bitwise operator that "cancels out" after being applied k times

Question

XOR is an operator that "cancels out" after being applied 2 times, in the sense that x ^ x = 0 for any x.

Is it possible to design (perhaps by composing XOR/AND/OR/NOT in some way?) a bitwise operator $, such that x $ x $ ... $ x (k xs in total) evaluates to 0 for any x?

Answer 1

Yes, for example if the $ operator is defined such that x $ y = 0 for any x or y, then it will have the property you describe.