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Subtraction is not associative. One cannot just move parentheses around like that with numbers either:

5 - (2 + 3) =/= (5 - 2) + 3

The same holds for elements of a vector space.




You are correct

I was about to say you were wrong, but you are correct, and it is a bit unintuitive why - https://www.quora.com/Is-vector-subtraction-associative


Maybe I'm missing the point here, but what's so unintuitive about subtraction (vector or scalar) not being associative? Counterexamples seem easy to find. For example, 1 - 1 - 1 is not the same as 1 - (1 - 1).




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