Why is $-i^3 = i$? Why is the value of $-i^3$ equal to $i$?
After experimenting, I got this result -
$-i^3=-i^2\cdot -i=1 \cdot -i=-i$
What is the error in my proof?
EDIT
Here is the original proof -
$$-i^3=\left(\frac1i\right)^3=\frac{1}{i^3}=\frac{1}{-i}=-(-i)=i$$

Wondering if you meant $(-i)^3$ or $-(i^3)$?
For the former, $(-i)^3=-i \times -i \times -i=-(i^3)=-[(i^2)(i)]=-[(-1)(i)]=i$. Note that $i^2=-1$.
For the latter, $-(i^3)=-[(i^2)(i)]=-[(-1)(i)]=i$.
So, both are the same; i.e., $(-i)^3=i=-(i^3)$.
