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Assertion (A): 0 has no multiplicative inverse. Reason (R): There is no rational number that, when multiplied by 0, gives 1. Which is correct?

Class 8Rational NumbersRational Numbers
  • ABoth A and R are true and R is the correct explanation of A
  • BBoth A and R are true but R is not the correct explanation of A
  • CA is true but R is false
  • DA is false but R is true

Step-by-Step Solution

0 times any number is 0, never 1, so 0 has no reciprocal. R is exactly why A holds.
Answer: A) Both A and R are true and R is the correct explanation of A

Key idea: Identities and inverses

**Additive identity**: 0. For any rational a: a + 0 = a.

**Multiplicative identity**: 1. For any rational a: a × 1 = a.

**Additive inverse** (negation): For a, the additive inverse is −a. Their sum is 0. So a + (−a) = 0.

**Multiplicative inverse** (reciprocal): For non-zero a = p/q, the multiplicative inverse is q/p. Their product is 1. **0 has no multiplicative inverse** (1/0 is undefined).

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