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ㄱ. $a \circledcirc 1 = a ^{2}$, $1 \circledcirc a = 1$이므로 $a \circledcirc 1 \ne 1 \circledcirc a$ (거짓) ㄴ. $\displaystyle \frac{1}{a} \circledcirc b = a ^{-2b}$, $\displaystyle \frac{1}{a \circledcirc b} = a ^{-2b}$이므로 $\displaystyle \frac{1}{a} \circledcirc b = \frac{1}{a \circledcirc b}$ (참) ㄷ. $\displaystyle a \circledcirc \left( \frac{1}{2} b \right) = a ^{b}$, $\displaystyle \frac{1}{2} \left( a \circledcirc b \right) = \frac{1}{2} a ^{2b}$이므로 $\displaystyle a \circledcirc \left( \frac{1}{2} b \right) \ne \frac{1}{2} \left( a \circledcirc b \right)$ (거짓)