Paper 1 · November 2010 · Groups

The set $G = \{0, 1, 2\}$ forms a group under addition modulo 3. State the identity element.

Model answer

Also accepted: e=0, zero

Explanation

Adding 0 to any of 0, 1 or 2 and taking the least non-negative remainder on division by 3 returns the same element, so 0 leaves every element unchanged and is the identity.

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

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The set G={0,1,2}G = \{0, 1, 2\}G={0,1,2} forms a group under addition modulo 3. State the identity element.

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The set $G = \{0, 1, 2\}$ forms a group under addition modulo 3. State the identity element.