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Paper 1 · November 2010 · Groups

In the group $G = \{0, 1, 2\}$ under addition modulo 3, find the inverse of the element 2.

Model answer

1

Also accepted: one

Explanation

The identity is 0, so the inverse of 2 is the element that adds with it to give 0. Since

2+1=3

and 3 leaves remainder 0 on division by 3,

2+1\equiv 0 \pmod 3

, so the inverse of 2 is 1.

Derived from ZIMSEC Further Mathematics 9187/1, November 2010, Q5

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