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Properties of Multiplication of Integers

The product o...

Question

The product of two negative integers is

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Solution

The product of two negative integers is a positive integer.
Example $: (- 2) \times (- 2) = + 4 .$
Hence $,$ The product of two negative integers is positive $.$

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Q. Which of the following statements are true and which are false?

(i) The product of a positive and a negative integer is negative.
(ii) The product of two negative integers is a negative integer.
(iii) The product of three negative integers is a negative integer.
(iv) Every integer when multiplied with −1 gives its multiplicative inverse.
(v) Multiplication on integers is commutative.
(vi) Multiplication on integers is associative.
(vii) Every nonzero integer has a multiplicative inverse as an integer.

Q. Which of the following statements are true?
(i) The product of a positive and a negative integer is negative.
(ii) The product of three negative integers is a negative integer.
(iii) Of the two integers, if one is negative, then their product must be positive.
(iv) For all non-zero integers a and b, a × b is always greater than either a or b.
(v) The product of a negative and a positive integer may be zero.
(vi) There does not exist an integer b such that for a> 1, a × b = b × a = b.

Product of two negative integers is:

The product of two negative integers is always _________integer.

The product of three negative integers is a __ integer.

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