\(Key\,\, of\,\, C\)Notice how the fingering is the same with the exception of one finger moved one whole step.
\(C\,\, (I,\,\, root\,\, inv.):\,\,\underline{C},\,\,E,\,\,G\,\,\)
\(\longrightarrow\)
\(A\,\,m\,\,(iv,\,\, 1st\,\,inv.):\,\,C,\,\,E,\,\, \underline{A}\)
\(Key\,\, of\,\, C\,\,\sharp\)
\(C\,\, \sharp\,\,(I,\,\,root\,\, inv.):\,\,\underline{C\,\,\sharp},\,\,F,\,\,G\,\,\sharp\)
\(\longrightarrow\)
\(A\,\,\sharp\,\,m\,\,(iv,\,\,1st\,\,inv.):\,\,C\,\,\sharp,\,\,F,\,\, \underline{A\,\,\sharp}\)