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Algebraic Identities

If the number...

Question

If the number of negative integers in the product is odd then the product is ______

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Solution

If the numbers of negative integers are to be multiplied are even in the number
Eg $- 2 \times - 2 \times - 2 = - 8 - 2 \times - 2 \times - 2 \times - 2 \times - 2 = - 32$
As we see the numbers are to be multiplied are odd so the product at last is negative

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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.

Q. Which of the following statements are true and which are fals?
(i) The product of a positive integer 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.

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.

Give an example to show that the product of

(a) an even number of negative integers is positive .

(b) an odd number of negative integers is negative.

If the number of negative integers in the product is even then the product is ______

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