A5. Choose $a$ so that the value of the expression $\left(1-\left(1-a^{-1}\right)^{-1}\right)^{-1}$ is 3.
(A) $a=-2$
(B) $a=2$
(C) $a=\frac{1}{2}$
(D) $a=30$
(E) $a=0$
A5. The equation $\left(1-\left(1-\frac{1}{a}\right)^{-1}\right)^{-1}=3$ can be rewritten as

$$
3=\left(1-\left(\frac{a-1}{a}\right)^{-1}\right)^{-1}=\left(1-\frac{a}{a-1}\right)^{-1}=\left(\frac{a-1-a}{a-1}\right)^{-1}=\frac{a-1}{-1}=1-a
$$

and we get $3=1-a$ or $a=-2$.