Calculating output impedance of Vbe multiplier
Since we have seen some different approaches to arrive at the (correct) solution, here comes my version:

1.) From feeback theory we know that r,out=r,open/(1-LG)
    (with r,open: output resistance without feedback; LG=Loop gain).

2,) For calculation of r,open and LG we open the feedback loop at a point which does not require a load mirror (no loading errors due to opening): Such a node is at the base because r,be may be assumed to be infinite (ib=0 because of beta infinite). 

3.) From simple inspection: r,open=R1+R2  and LG=-gm*(R1+R2)*R2/(R1+R2)=-gm*R2.

4.) Inserting into the expression under 1) gives r,out=(R1+R2)/(1+gm*R2).

5.) Setting gm=Ic/Vt=0.235 A/V we have r,out=25.4 ohms.