In the expression, $a \$ b,$ the $\$$ symbol represents one of the following arithmetic operations on $a$ and \(b\

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In the expression, $a \$ b,$ the $\$$ symbol represents one of the following arithmetic operations on $a$ and $b$ (in the order the variables are shown): addition, subtraction, multiplication, and division. Given that it is not true that $a \$ b = b \$ a$ for all possible values of $a$ and $b,$ a pair of nonzero, non-identical values for $a$ and $b$ is chosen such that $a \$ b$ produces the same result, no matter which of the operations (under the given constraints) that $\$$ represents. The nonzero value of $b$ that cannot be chosen, no matter the value of $a,$ is

A. $-2$

B. $-1$

C. $-\dfrac12$

D. $1$

E. $\dfrac12$

Answer: D

Source: Manhattan GMAT

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