What is additive inverse and multiplicative inverse ? Explain with one example .
Answers
Answer & Explanation:
1. An additive inverse of a field element a is an element b such that a+b=b+a=0. It turns out that only one additive inverse exists for each element.
For example, over the rational numbers, the additive inverse of 25 is −25 and the additive inverse of −5 is 5.
2. For a field element a not equal to 0, a multiplicative inverse of a is an element b such that a⋅b=b⋅a=1. It turns out that only one multiplicative inverse exists for each element.
For example, over the rational numbers, the multplicative inverse of 2/5 is 5/2 and the multiplicative inverse of −1 is −1.
Step-by-step explanation:
Additive inverse:-In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite, sign change, and negation. For a real number, it reverses its sign: the opposite to a positive number is negative, and the opposite to a negative number is positive. Example:- the additive inverse of the positive number 5 is -5
Multiplicative inverse:- in mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x⁻¹, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the number. Example:- For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4.
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