Manipal MET2013MathematicsMathematical Induction
If G is an abelian group then for all a, b Gb⁻¹ * a⁻¹ * b * a is equal to
Options
- Aa * b
- Ba^ -1 * b⁻¹
- Ce
- DNone of these
Correct answer
C. e
Step-by-step solution
b^ -1 * a^ -1 * b^ a= (b^ -1 * a⁻¹ )^ (b^* a )= (a^ b )⁻¹ ^* (b^* a )= (a^* b )^ -1 * (a^* b )=e .