Three standard facts about the partial correlation $r_{12.3}$

If $r_{12.3}$ is the correlation coefficient between the variables $X_1$ and $X_2$ after eliminating the linear effect of $X_3$, then which of the following are correct? (1) $-1\le r_{12.3}\le1$; (2) $r_{12}^2+r_{13}^2+r_{23}^2-2r_{12}r_{13}r_{23}\le1$; (3) $r_{12.3}^2=b_{12.3}b_{21.3}$, where $b$'s are partial regression coefficients.