Question

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.

Answer 1

(i) True.
(ii) False. Since the number of negative signs is even, the product will be a positive integer.
(iii) True. The number of negative signs is odd.
(iv) False. a $\times$ (−1) = −a, which is not the multiplicative inverse of a.
(v) True. a $\times$ b = b $\times$ a
(vi) True. (a $\times$ b) $\times$ c = a $\times$ (b $\times$ c)
(vii) False. Every non-zero integer a has a multiplicative inverse $\frac{1}{a}$, which is not an integer.