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Properties of Multiplication of Integers - Multiplicative Identity

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Multiplicative Identity:

We know that 1 is the multiplicative identity for whole numbers.

Statement

Observation

( - 3) × 1 = - 3 1 is the multiplicative identity for integer.
1 × 5 = 5 1 is the multiplicative identity for integer.
( - 4) × 1 = - 4 1 is the multiplicative identity for integer.
1 × 8 = 8 1 is the multiplicative identity for integer.
1 × ( - 5) = - 5 1 is the multiplicative identity for integer.
3 × 1 = 3 1 is the multiplicative identity for integer.
1 × (- 6) = - 6 1 is the multiplicative identity for integer.
7 × 1 = 7 1 is the multiplicative identity for integer.

This shows that 1 is the multiplicative identity for integers also.

In general, for any integer we have, a × 1 = 1 × a = a

Statement

Observation

3 × (− 1) = −3 (–1) is additive inverse of an integer.
(- 3) × (− 1) = 3 (–1) is additive inverse of an integer.
( - 6) × (− 1) = 6 (–1) is additive inverse of an integer.
(- 1) × 13 = - 13 (–1) is additive inverse of an integer.
(- 1) × (− 25) = 25 (–1) is additive inverse of an integer.
18 × (− 1) = - 18 (–1) is additive inverse of an integer.
(−1) × 225 = −225 (–1) is additive inverse of an integer.
(−316) × (−1) = 316 (–1) is additive inverse of an integer.

0 is the additive identity whereas 1 is the multiplicative identity for integers. We get the additive inverse of an integer a when we multiply (–1) to a, i.e. a × (– 1) = (– 1) × a = – a.

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