Today, while perusing the literature, I encountered a perplexity. The field $F$ is a finite field composed of $q$ elements, and $F^*= \{a_1, a_2,\dots, a_{q-1}\}$. However, I am unsure why $a_{1}a_{2}\cdots a_{q-1}=-1$. The literature directly provides this result, but the reason behind it is unclear to me. Currently, I am aware that the multiplicative group of any finite field $F$ is a cyclic group. I am uncertain whether this property can be utilized to deduce $a_{1}a_{2}\cdots a_{q-1}=-1$. Hence, I raise this question.
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