Correct equation for describing *exactly* the output of a current follower
I suspect that the second equation was supposed to be:

$$v_0=-i_iR_f+i_bR_f-\frac{v_o}{A} \tag {2}$$

In other words:

$$v_0=-R_f(i_i-i_b)+v_s$$

This emphasizes the fact that in the non-ideal case, \$v_s\$ is no longer exactly 0.