I've been assigned to prove $$ A \exp(-iB)A^{-1} = \exp(iABA^{-1}) $$ for $A$ being anti-unitary and $B$ Hermitian.
To my understanding, I should simply expand the exponent, insert a bunch of $1=AA^{-1}$, and commute $Ai=-iA$ when moving $i$ to the left in each term.
Question: why do I need to know that $B$ is Hermitian? Am I missing something?