Q88 / 180 · KCET 2010 · Mathematics
The inverse of 2010 in the group $\mathrm{Q}^{+}$of all positive rational under the binary operation * defined by $\mathrm{a}$ * $\mathrm{b}=\frac{\mathrm{ab}}{2010}, \forall \mathrm{a}, \mathrm{b} \in \mathrm{Q}^{+}$, is
- A2009
- B2011
- C1
- Correct answerD2010
Solution
By inspection of binary operation $(*)$ over;
$$
\mathrm{a} * \mathrm{~b}=\frac{\mathrm{ab}}{2010}, \forall \mathrm{a}, \mathrm{b}, \in \mathrm{Q}^{+}
$$
2010 is the identity element.
And also we know that, the inverse of identity element is itself identity element.
Hence, inverse of $2010=2010$
Hence, the correct answer is option: 'D'.