If a, b are positive integers, where in the (modulo 7) with the multiplication operation, then inverse of 3 in the group is?
- 4
- 5
- 3
- None of these
Explanation
To find the inverse of 3 in modulo 7, we need to find a number x such that:
3x ≡ 1 (mod 7)
We can try multiplying 3 by each number from 1 to 6:
3 × 1 = 3
3 × 2 = 6
3 × 3 = 9 ≡ 2 (mod 7)
3 × 4 = 12 ≡ 5 (mod 7)
3 × 5 = 15 ≡ 1 (mod 7)
So, the inverse of 3 in modulo 7 is 5.
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