I'm currently reading a textbook to do with curvature and $k$-forms.
It says that the curvature $2$-form given connection $1$-form, $A$, is $$F =d^A A = dA+A \wedge A$$
It then goes on to say that the covariant exterior operator, $d^A$, acts on $k$-forms, $\Omega$, via $$d^A \Omega =d \Omega + A \wedge \Omega + (-1)^{k+1} \Omega \wedge A$$
If we let $\Omega=A$ we get two different formulas$?$ I'm just getting really confused by this, any help?