quick differential forms question

Question

I know that for a 1-form A,

$$ dA=-Ad $$

where d is the exterior derivative (and in my expression on concern it will be acting on something else to the right no worries).

But what about 0-forms? Does the same hold?

$$ dU=-Ud $$

for a 0-form U.

Answer 1

Ah, sorry, what is on the left does indeed matter.

Consider the identity from this 0-form U I had above,

$$ \begin{eqnarray*} U U^{-1} &=& 1 \\ d(U U^{-1}) &=& d(1) \\ d(U)U^{-1} + U (d U^{-1})&=& 0 \\ d(U)U^{-1} &=& - U (d U^{-1}) \end{eqnarray*}$$

This was my fault in only looking into the dA=-Ad applied to 0-forms without considering what the d now acts on to the right.