notes
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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