Question

Which of the following statements are
true and which are false?
(1) The product of a positive and a
negative integer is negative.
(2) The product of two negative Integers
is a negative integer.
(1) The product of three negative Integers
is a negative integer.
(3) Every Integer when multiplied with -1
gives its multiplicative inverse.
(4) Multiplication on Integers is
commutative.
(5) Multiplication on Integers is
associative.
(6) Every nonzero integer has a
multiplicative inverse as an integer.​

Answer 1

Answer :-

(1) The product of a positive and a

negative integer is negative. = True

= Every positive integer when multiplied by any negative integer gives the product in negative.

For eg :- 2 × (-3) = -6

(2) The product of two negative Integers

is a negative integer. = False

=> The product of two negative integer is always a positive integer. For eg :- (-2) × (-3) = 6

(3) The product of three negative Integers is a negative integer. = True

=> The product of three negative numbers gives a negative number. For eg :- (-2) × (-3) × (-4) = -24

(4) Every Integer when multiplied with -1

gives its multiplicative inverse. = True

=> When an integer is multiplied by (-1), the product is it's additive inverse. For eg:- Additive inverse of (-2) is 2

(5) Multiplication on Integers is

commutative. = True

=> Even when the order of the integers are changed, the product will be the same. For eg :- (-5) × 2 = 10 or, 2 × (-5) = 10. Both gives the same results.

(6) Multiplication on Integers is

associative. = True

=> When the integers are re grouped, it won't change the product. For eg :- (5 × 3) × 2 => 15 × 2 = 30 or, 5 × (3 × 2) => 5 × 6 = 30. Hence, it gives the same answer.

(7) Every non-zero integer has a

multiplicative inverse as an integer. = True

=> Every non zero integer has a multiplicative inverse also known as reciprocal. For eg:- Multiplicative inverse of 5 is 1/5.