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Then the product of two nonunits in ℤ𝑛 may be a unit. True or false

Question

Then the product of two nonunits in ℤ𝑛 may be a unit. True or false

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Solution

True. In the ring ℤ𝑛, the product of two nonunits can indeed be a unit. For example, in ℤ4, neither 2 nor 2 are units, but their product, 4, is equivalent to 0, which is a unit in ℤ4.

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Given that𝑓(𝑥)=2𝑥−3 and 𝑔(𝑥)=1−𝑥4solve (𝑓∘𝑔−1)(𝑥)=(𝑓∘𝑔)(𝑥).

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