Assume we have two frames, A and $B,$ and we know the representation of the $B-$frame

basis vectors in the A frame $($i$.$e$.,$ we know each hat$(b{)}_{i,A}$ written as a linear combination

of the $A-$frame basis vectors$).$ Write the expressions for the direction cosine matrices

$BA$ and $AB$ in terms of hat$(b{)}_{1,A},$hat$(b{)}_{2,A},$ and hat$(b{)}_{3,A}.$