Answer
Yes, $a=-1$ or $a=1$
Work Step by Step
We know that $a^{-1}=\frac{1}{a}$.
So, if we know that $a^{-1}=a^{1}$, then we also know that $a=\frac{1}{a}$ for some number a. Therefore, the number a will have to have the same value as its reciprocal, and we know that -1 and 1 are the only numbers that satisfy this condition.
Therefore, $a=-1$ or $a=1$.
