KCET2013MathematicsMathematical Reasoning
In Ine (Z, *), if a^ * b=a+b-n, a, b Z, where n is a fixed integer, then the inverse of (-n) is
Options
- An
- B-n
- C-3 n
- D3 n
Correct answer
D. 3 n
Step-by-step solution
Given, In a group (Z, ^ * )a^ * b=a+b-n, a₁, b z...(i) where, n is a fixed number array llr & a^ * e=a & & a+e-n=a [from Eq. (i)] & e=n & (identity) array For finding inverse, ^ * (-n)=n -n-(-n)=n [from Eq. (i)] -n-n=n =3 n So, inverse of (-n) is 3 n .