Question

Which of the following statement(s) is/are correct about the property of multiplicative inverse?
(i) For an integer $a$, the multiplicative inverse is $\frac{1}{a}$.
(ii) The product of an integer and its multiplicative inverse is $1.$
(iii) The multiplicative inverse of $-67$ is $\frac{1}{67}$.
(iv) The integers $1$ and $-1$ are also their respective multiplicative inverse.

Answer 1

(i) For an integer $a$, the multiplicative inverse is $\frac{1}{a}$.

This is the definition of multiplicative inverse. So, this is correct.

(ii) The product of an integer and its multiplicative inverse is 1.

$a$ $\times$ $\frac{1}{a}$ $=1$. So, this is also correct.

(iii) Multiplicative inverse of 67 is $\frac{1}{67}$.

Multiplicative inverse of -67 is $-\frac{1}{67}$. So, this is incorrect.

(iv) The integers 1 and -1 are equal to their resepective multiplicative inverse.

Multiplicative inverse of 1 is 1 and that of -1 is -1. So, this is correct.

Hence, statements (i), (ii) and (iv) are correct.