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with. Let’s take a = 2, b = 3 as two scalars and v = (1, 5) as a vector. Then (ab)v = [(2)(3)](1, 5) = 6(1, 5) = (6, 30). On the other hand, 2(3(1, 5)) = 2(3, 15) = (6, 30), which gives the same result. These examples not only help us understand how these properties work but also reinforce our