ϵr={{ϵ,0,0},{0,ϵ,0},{0,0,ϵ}}
Arc={{Cos[θ],Sin[θ],0},{-Sin[θ]/ρ,Cos[θ]/ρ,0},{0,0,1}};
Arct=Transpose[Arc];
detArc=1/ρ;
ϵc=Simplify[Dot[Dot[Arc,ϵr],Arct]/detArc]
Acr={{Cos[θ],-ρ*Sin[θ],0},{Sin[θ],ρ*Cos[θ],0},{0,0,1}};
Acrt=Transpose[Acr];
detAcr=ρ;
ϵr2=Simplify[Dot[Dot[Acr,ϵc],Acrt]/detAcr]